I've been to almost every state in the u.s. and many big cities. I'd suggest L.A. if you want warmth and adventure. I've only been there for a couple of days but it seemed much more interesting than I'd expected, much prettier than I thought it would be also. Plus, SF and San Diego aren't too far. Never been to San Diego but SF is every bit as interesting as its reputation had led me to believe. I think Las Vegas isn't too long a bus ride away either. Even if, like me, you don't drink or gamble, it's worth seeing once. No place else like it on earth. Even if you hate it you'll probably still be glad you saw it.
If you're traveling in the summer every city can be hot. I live in Chicago which is well north and it's common for it to be in the 80s and near 100 isn't unheard of. If you'll be here in the summer I'd just stick to the east coast, there are many large and interesting cities that are easy to reach by train or bus, Boston, Washington, New York, Philidelphia, Baltimore and so on. Absolutely go to New York if you want a true urban experience, there is no larger or diverse or interesting city in the US. It is the king of American cities.
If you're traveling in the summer every city can be hot. I live in Chicago which is well north and it's common for it to be in the 80s and near 100 isn't unheard of. If you'll be here in the summer I'd just stick to the east coast, there are many large and interesting cities that are easy to reach by train or bus, Boston, Washington, New York, Philidelphia, Baltimore and so on. Absolutely go to New York if you want a true urban experience, there is no larger or diverse or interesting city in the US. It is the king of American cities.