[X] Spend the day at Arsenal Pier, it's creepy and mostly closed down in the offseason but it's free. And nice and rainy. And with so few people around it means there's nobody there to watch you be disgustingly affectionate in public.
[X] The city's got a few museums, a zoo, and an aquarium, and admittance is basically a pittance during the middle of the week. Pick one, hell pick two, and just kill all the time from morning to afternoon feeling all cultured and shit.
[X] Awkwardly ask Sebastian if he wants to go to the movies, you've bummed enough of an allowance from Winter at this point that you can probably make a matinee. Be nice to see something still in theaters for a change.