Could you define what you mean by "cool things"? It's kind of hard to advise you. If you are finding NYC not exciting enough for you, I'm having a hard time thinking of places to suggest.
LA has cultural attractions and a lively arts scene, but everything is quite spread out and you spend a lot of time in the car. Housing costs are high.
SF is prohibitively expensive (see above) and is less exciting than NYC.
The southwest has amazing scenery and hikes, but cultural attractions are quite scattered and you'd have to be into the outdoors. Also might be too hot for much of the year.
Chicago has a lot going on, certainly, but it is boiling in summer and freezing in winter. If not for the weather, though, it might be a good place to try.
Austin has a great music scene and warmer weather.
New Orleans has very humid, hot weather and a very high crime rate, but it is like no other city in the U.S.
I wouldn't call Jacksonville a cultural mecca, but to be fair, I've never lived there and don't know much about it.