How much does living further away affect "experiencing the city?"
Honestly, it doesn't. I have lived in midtown Manhattan right on Columbus Circle and it was great but tourists are annoying after a while. During my broke days I lived in east flatbush and hated it, NEVER move there lol. but now im in midwood and im exactly 30 minutes to the greenich village where fun stuff happens, i guess? I don't do touristy things, but my friends and I hang out at different places either in the city or brooklyn, or my SO and i like to go on dates to nice places which are present in both boroughs. Again, I don't like Queens so i never go there so can't say what its like commuting from there.
I needed my VERY large apartment with my own washer dryer, dishwasher, balcony extra bedroom and bathroom after a point, so my husband and i decided we should move away from the city, i live next to an express train so i never have a problem getting into the city. However please note, the MTA sucks, you will hate yourself for taking the subway, for no reason other than the subways can be super incompetent. Theyre great, but they are old like pretty much everything in NYC, so they get delayed, they get stuck underground they might not have air conditioning during the summer etc etc etc so you can just hate life because of them sometimes, despite them being 24hrs and convenient... That being said, look at whats important to you.
Ask yourself do you want to be in the west village living in a shoebox for $3500 or more (youre not going to pay less than that for a small appt in lower Manhattan). Or do you want more space for $2000. The east side is cheaper than the west, why i really don't know. I don't like the waterside plaze location, it wasn't for me. My friend has been living there her whole life and loves it.
Do you mind commuting 30-45minutes door to door, or do you get repulsed by the idea? Do you have kids? Do you need parking spots for your car? Can you afford it? Is it close to the subway (most important)!!!?
There Sty Town too and Peter Cooper village, its broker fee free.
I would also suggest you visit new york, and you get on cityspade, zillow, streeteasy (i found my new place on streeteasy as it shows more apts with no brokers fee) and look for a place, go to neighborhoods, make a budget, if you're moving from American (lol) to NYC get prepared to realize the things you had are probably luxury items here for instance a washer/dryer in the unit. Hate washing dishes? good luck because old apartments don't tend to have them.
Take a tour of nyc, avoid times square like the plague, spend time on the subway, see what you want to experience, and how close you want to be to it.
Having said that I LOVE my city <3
and welcome to the Empire State!