Do you want fresh air and park space, and a fast commute to Midtown? If so, then it's tough to beat UES/UWS. Pick whichever gives you the shorter commute. They're not the very best for going out, but are 15 min away on an express train. Plus they're a bit cheaper and arguably the most beautiful neighborhoods in the city.
If you don't care about fresh air or park space, try Murray Hill or thereabouts
If working in FiDi, Chinatown and Wall St are good options. They're young, high earning neighborhoods full of great places to go out
Weird that nobody mentioned Jersey City. Though not technically NYC, it's just across the river and the commute through the metro is not bad. 20min to downtown and 30min to midtown. Beware of weekend slowdown of metro tho. Safe neighborhood with new buildings filled with yuppies. A little bit of income tax benefits too.
Any answer would be subjective unless former criteria is specified. And even then. But it Doesn’t matter which neighborhood is best because with that budget you can’t own there. If we’re talking Manhattan, I’ve lived in UES, UWS, East village and West Village and all of them have had advantages and disadvantages. Where will you be commuting to?