It wouldn't be very random if that's guaranteed to happen; you're exactly as likely to encounter a MG as you would on, say, a hospital or NYPD run. No, it's exactly what it says: exploring so you aren't totally clueless about what's around the place you now live. It might help you remember, say, restaurants to bring friends, or what landmarks are close to your home.
EDIT: Bringing your pets along would scream "magic" to those in the know, though, increasing the odds of a MG encounter along that route (but by no means guaranteeing it).
I mean, I don't see why. Despite what people might think, you can train dogs not to run off without a leash. Working dogs have done so for centuries. Cats are a bit more iffy, but I know my uncle used to have a cat trained to travel with him by riding on his shoulder. The birds might be a give-away, if they stick close enough. I figured they'd be up high enough to not be noticed, though.
Basically, I think we might look kinda weird...but then, this is New York City. They see weirder sh*t than someone walking cats and dogs and birds pretty regularly. Nothing we'd be doing is inherently magical.
We don't want to talk to magical girls! How many times does
@Alivaril have to say that the magical girls are the fucking mob?
Some of them act like mobsters in some situations. Doesn't mean they always act like assholes. Or even are necessarily assholes. Like IRL mobsters, their extortion and other such behavior may "just be business". Not saying that's a good thing, mind, just that they may act completely differently "off-duty". People who commit crimes as a job aren't by default going to carry over that mentality into all social situations. And they do tend have their own codes of ethics, no matter how contorted. There's a reason pedophiles have such a hard time in prison.
I know you weren't talking to me, but I felt like I should reply since I advocated this option.
Anyway, the idea behind warding hospitals is not that it will make magical girls leave us alone because we're such good people. The idea is that going public with a verifiable means of testing our wards is a way of quickly telling lots of magical girls at once about us. Lots of magical girls from lots of different groups. The idea is that if one group snatches us and denies us offering our services to other groups, then all the other groups will come after them.
That's why I prefer the idea of warding hospitals over police stations, because hospitals are more open for magical girls to enter and test out. Also, some magical girls may have friends/relatives in the hospital, and thus may be more kindly inclined to us.
I don't know why we're going public at all. I got the vague impression that we're still in the "no one knows what the flying f*ck happened in Mitakihara" stage of the masquerade breaking down. Until things have progressed further, I see no reason to be the person who went public. At the very least, let things stew for a day or two before we start pulling this kind of thing.
If I'm wrong, and talking to the magical girls doesn't require any preparation, we spend some time doing something we were already going to do but we do it in a different order. If you're wrong, you're fucking us over.
We have Word of God that the primary challenge in the early game for a Green/White mage is dealing with the gangs:
Every piece of evidence we have, in character and out of character, says that your idea of going out and meeting friendly magical girls is a pipe dream. If you want to see money-making simulator, try the miserable slog it'll be to gather enough mana and skill to wipe out the gang that's oppressing us while being oppressed and trying to conceal the fact that we're not actually a magical girl. Protection rackets are not fun. They are not a way to make friends. They do not open up interesting strategic options. That are, in fact, the single most prominent piece of game-state that has been constructed as an obstacle for us to overcome in the early-game. Dealing with the gangs and the demands they make will be unpleasant and stressful and it will routinely prevent us from doing things we want to do. We will have to schedule every decision we make around it, if for no other reason than we'll have to spend a significant fraction of our time hunting instead of doing useful things.
It is entirely possible to make mistakes. Alivaril is not here to satisfy your wish fulfilment fantasies. Some options won't do what you want. Some options are simply better - or worse - than others. There is a world and logic holds. He may put a thumb on the scales sometimes, and our main character may veto particularly obviously dumb ideas, but if you vote to, say, focus on grinding Summer Raiment without laying any Hallowed Havens at all, he's not going to hesitate to let you make life difficult for yourself. Remember: His last attempt at this quest bad-ended because he did not properly explain the challenges and we fucked up hard enough to make the quest unwinnable.
If you're going to insult anything other than your own blind naivete as "money-making simulator", by the way, I recommend you reread Alivaril's posts so far, think about them a bit, and then leave, because you're not going to enjoy this quest. If nothing else, stop trying to derail the quest before your self-centered attempt to dictate reality fails and bad-ends it again. Our early-game will revolve around our need to build enough personal power to be too strong to bully. The mid-game will be to pivot from personal power into taking over NYC's magical community. The endgame will be a mad scramble to improve our economy and military as civilization collapses under increasing witch load and we prep to fight the impending super-witch while finding a way to kill Kyubey. Here, I'll make it easy for you:
I don't even disagree on that, V. However, Alivaril has already stated that we may not encounter an MG if we explore. And running into a stray MG isn't running into a band of them. Nor does it mean they'll automatically know we have magic. Sure, our pets are on the high end of well-trained, but that alone isn't a sign of magic, persay. You can actually train cats to come when called, though it's not 100% effective. Hell, my current cat tends to follow people's feet too closely, and cut in front of people when he thinks he knows where they're going. Hence why we refer to him as "mobile tripping hazard".
Birds I know much less about, but I can't imagine falconers keep them on jesses constantly. That would make hunting with them hard. As such, I assume they may also be trained to come when called. So we may just look like a wandering animal trainer and her pets. Odd, to be sure. But it's NYC.