Fusion drives would get us to nearby star systems in reasonable timeframes, laser high ways would let us travel around the galaxy at near light speeds. even without FTL we are not trapped in the sol system... even if we never crack fusion, or long distance spaceflight we could still jump from rock to rock on the oort cloud, using objects like pluto and makemake to build far out colonies to resupply,... and that gets you out light years, from where you can jump to another star systems oort cloud and work your way into the system taking short hops all the while.
With basically current tech you could colonize the galaxy it'd just be expensive and take a long time so no one is interested at the moment. Not all the GDP of the world expensive either, but longer than humanity has existed long times.
Spend say 5% of the US budget on building a large and capable moon base that is mostly self sustaining and does it's own mining, refining and smelting, an industrial base capable of supporting itself and build rockets and supplies. The moon has a lot less gravity so it's easier to launch from there, and it'd serve as a stress test for all involved technologies and factors. By the time it is finished you could build a viable outpost on almost any airless rock. This would take a few decades even with that level of commitment most likley, but from the moon base hop onto the asteroid belt or similar and just keep expanding out. A century or two and you will be hopping along the oort cloud... and from there you will reach other stars since the oort clouds practically touch.
You've sort of kind of restored the plausibility of CJ Cherryh's introduction to
Downbelow Station there, albeit with the string of star stations developing not at actual stars separated by handfuls of light years, but on a much smaller scale stringing together much much smaller cosmic objects. Of course her "merchanter" society depended on actually relativistic semi-generation ships becoming Family sublighters (and then no stories are set in that era, she pulls the traditional SF rabbit out of the hat of a functioning FTL drive being developed eventually to revolutionize the centuries-old starfaring society first built by the sublighters). Still something not entirely unlike her prologue can happen in your terms, so that is something.
I don't think a fusion drive using onboard propellant can reasonably attain speeds much faster than 1/10 C, and even that involves a mass ratio of e each burn; there have to be two such to boost up to the cutoff speed and then brake down to encounter the target object as anything other than a projectile--possibly I am overlooking feasible means of braking against galactic magnetic field lines or whatnot which saves us one of these burns, but assuming we have to do it all the hard way, that's a mass ratio of 7 to get to a speed allowing us to get to the Alpha Centauri system in...a bit under half a century. To assert then that fusion alone can allow "interstellar" travel is to either assume humans somehow shifting over to a much longer timeframe than we are accustomed to or capable of living as of yet--suspended animation and/or life extension, presumably actually both since even if I can life a thousand years it is hard to see me blithely accepting being cooped up in a starship for a century of that time or more. Or as you do, shift attention away from defining "star travel" as literally going from star to star and being content with exploring the darker and nearly but not quite void spaces in between.
My assumption about fusion is based on the general sense that one releases about 1 percent of the rest mass energy in typical fusion processes, and this energy if fully applied to the waste "daughter" products of the reaction would enable it to be ejected at just about 1/10 C, which in turn would if plugged into the rocket equation (no need to develop the relativistic rocket equation at these speeds, Newtonian approximations are close enough for government work here) give delta-V equal to the exhaust velocity when one has expended 1-e of the initial mass. At a full G thrust this would take about 1/10 of a year.
If only we had some convenient way to sustain full G thrusts for say 3-4 subjective years at reasonable mass ratio costs, and could also deal with the side consequences (sleet of interstellar particles manifesting as intense cosmic ray like bombardment, not to mention turning into a cloud of hot plasma if one encounters anything as substantial as say a paperclip out there, stuff like that) then we could count on relativistic time contraction to shorten the time frame of journeys of many tens of light years which puts oodles of star systems in more conceivably convenient reach--to the subjective experience of the crew of the ship, when they go home again they arrive as many years later as the round trip distance in light years plus a year for boosting up to and back down from near C as seen by these stay at homes. But many a fun SF epic has been written centered around interstellar trader societies that skim the centuries of human history in this way.
Alas, even if we had a magical gadget that simply converted every gram of mass fed into it directly into a semicollimated shower of photons (or less destructively neutrinos, though I have wondered whether a mass flux of neutrino exhaust sufficient to drive a ten thousand tonne interstellar ship at 1 G thrust would in fact still vaporize something that strayed into the immediate exhaust flow--neutrino interactions are incredibly rare but cram enough of them into a tight volume and you are still going to heat things up! Question is, how many, in a per kilogram sense) which gives us the maximum specific impulse physics as I understand it allows for in a rocket, such that thrust is simply the energy flux divided by C, or alternatively the mass flow times C, the basic rocket equation (now we need to go relativistic, but I understand Taylor's Space Time physics these modified rocket equations are actually just hyperbolic functions, pretty simple) still would require a mass ratio of 7 to boost for two onboard subjective years, and then another factor of 7 to brake for overall factor of 50, and meanwhile we have all those liabilities of blasting through galactic space with its single atom per cubic meter mass densities turning into something really nasty at these relativistic speeds. If we boost for just half a year and coast, we are now going at approximately half C and have rather little relativistic time contraction to show for it yet, and we still need a mass ratio of 7 to both speed up and slow down. Not to mention we have no practical devices that we can do more than vaguely foresee being able to make, and would require stuff like storing half that reaction mass as antimatter. Lotsa luck with that! We know how to make it--it is just very very hard to do, and if we do it, storing it is pretty nerve wracking.
Mind, I did catch your suggestion that we could have laser drives of some kind that get around this mass ratio hitch by means of supplying the reaction mass from outside the ship--someone else pays for it as it were. But this would be a solution that would have to be built first, it is no good for our generation that hasn't built it yet, not to mention I can only imagine the havoc splashing powerful light beams around the Galaxy like that might wreck if anything goes wonky or someone gets hotheaded with them.
So you see why people would really like it if someone came along and said lookit, I just made a Jump drive that can take us to Tau Ceti and back in just an hour or so, most of that for launching from Earth and landing on the neat planet I found there (yeah, I know, Tau Ceti is supposed not to have planets alas, so much for my screen name).
I remain agnostic about that, and hold that if there is FTL, it won't practically be by means of the loopholes we currently speculate on, wormholes or whatever; these at best, like the laser interstellar highway, serve to connect points that are quite distant from where we are now, it can't take us from Earth to some random destination we name.
I suspect instead that if practical FTL for recognizably human people ever happens it will be a surprise of some kind requiring a new world view. And that world view has to somehow be consistent with the one we have, and perhaps there are ways of higher order understanding of how the universe is organized and structured that permit us to somehow square what we know already about spacetime with the possibility of me somehow being able to commute to Altair IV and back once a week without thereby enabling me to go back in time and kill Hitler or whatever. But I think I do understand why that is a taller order than it might seem, and that very possibly if we do derive some method of FTL, we will find time travel is a perfectly normal consequences. The fact that the universe does not disintegrate in paradoxes might be because of some kind of time travel constraints such as superdeterminism (no one will kill Hitler young because no one did, nor can one prevent that car accident nor show up in the reign of Cleopatra and scheme with her to take over the Earth using Nerf guns--because it didn't happen) or parallel universes (you can go hang out at the battle of Gettysburg all right, then skip ahead a year or so and stop Booth from shooting Lincoln, but the N space trajectory taking you there means you arrive at an alternate time line and when you try to return to 2020, you arrive in a completely different timeline and can never find your way home again--even if you carefully avoid interfering in any preventable way--meanwhile history as we know it is still out there somewhere unchanged by you because you missed it) or something weirder. But we can be confident that if FTL does mean we can now backtrack across our subjective past, some how or other the Cosmos gets over it and it is at most a subjective problem; if we can do FTL by any hook or crook, being able to do that is part of how the Universe actually normally works, one we happen to have been ignorant of hitherto. It might involve mind-bending challenges to our comfortable notions of causality but it cannot involve breaking the Universe!
I must of course defer to others who have advanced in their understanding of detailed current theory far beyond me.
But I stick to one of Clarke's laws, stated in weaker and more reasonable form than he did:
When a distinguished but elderly scientist assures you that a thing is possible, they are almost certainly correct, but if they insist that it is impossible, they may well be quite mistaken.
