I recommend New Orleans. Music in the streets. Restaurants post their menus outside in the afternoon. You can take the trolly to Audubon Park (named after illustrious homie James Audubon) where there is a running circuit with cross-training equipment spaced at intervals. And there are Museums: one of the 3 original copies of the Louisiana Purchase is on display there.

I once did a night stay at a cabin just off the Appalachian trail in West Virginia!

New Orleans is a great city full of history and interesting things to see.

blueridge mountains would be beautiful and maybe a little cooler.

The state parks in West Virginia have cabins you can rent relatively cheaply. My family and I used to go to Cabwaylingo every year, which is only about an hours drive from Huntington (where I live), which has an airport, a museum, lots of good restaurants and other things. I will say that Cabwaylingo is rather run down, but it's a good getaway. No TVs, no phones, almost no cell service. If you're interested, message me, and I'll find some more info for you.

I don't know how safe Central Park is and expect NYC lodging & museums will cost plenty .....it's sprawling nature and 2nd only to Paris for art/museums