east side neighborhood

Figure out which bridge you like to use and look near there. If it were me, I would look on the upper east side east of in the 80s/low 90s along East End Avenue/York or a bit west if you're willing to sacrifice some time in order to be closer to the subway. The FDR will get you to the 59th St. bridge/LIE quickly assuming no traffic, and you can get to the Triboro for a quick exit. You could try the 30s which gets you to the midtown tunnel but I feel like there is more traffic in that area generally and it's a bit less charming, imo.

FYI - York will eventually have an issue with garbage trucks once the marine transfer station is built but who knows when that will actually be done and if you're looking at rentals, it really won't make much of a difference to you short term.

I should have added 1st. It's easy enough to get to the FDR from 1st too. Lots of nice no fee luxury rental buildings there.

Check out the Sutton Place neighborhood. Right at the foot of the 59th Street bridge with access to all Manhattan has to offer, shopping, restaurants, theater and a quick taxi to the Upper Eastside and Museum Mile.