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I’m in NYC this summer and tons of people take the subway to work

Yeah taking the subway isn’t too bad, I’d aim for ~25min transport but if you have your place already, you know the specific timing. Just don’t be late ig!

Analyst and I have about a 30-35 min subway to work every day. East village/LES subway infrastructure sucks ass lol but cost of living is low

Definitely not a must to walk to work. Vast majority of people subway in the AM. I'd focus on 

1. having a ~20-25 min commute

2. no more than ~7 min walk to subway on either end (it'll suck in the winter)

3. Ideally no transfers; no more than 1 transfer if you have to

IMO I would stay on the west side for either of those banks - way easier to go up/down Manhattan than across town. Battery Park City is okay, parts of Fidi are a stop or two away on the subway, WV/Tribeca/Soho are obviously great but out of budget, western side of chelsea (not too west, some parts are like 15 min walk to subway), Hells Kitchen (same story, don't go too far west). You can get there from like EV or Murray Hill with a transfer, but it's so nice to have 1 train directly to work instead of transferring

In all likelihood you'll be taking Ubers home if it's late at night (after 9PM for most banks). A quick subway ride to work is no biggie, just be cognizant that every minute of commute is one less minute of sleep you'll get a night. I co-sign everyone who said look for somewhere that doesn't require a subway transfer. I commute from 28th to 50th street and it's only ~15 minutes with a brief subway ride.  

I live walking distance and I wouldn’t have it any other way. But most people do commute, a few analysts I see take citi bikes to work, quick train rides with Ubers home. Definitely just what you prefer, will be a non issue either way

I lived 7 blocks from the office when I did banking and I did appreciate the convenience of getting to and from the office. As others have mentioned, you will likely be Ubering home every night, so it's just whether you value an extra ~20 minutes of sleep in the morning.