Probably New York City or Washington D.C., but since I've never been to either (planning on going this summer), I'll give you my opinion for places I have gone:
Best city to live in: Irvine, California
Amazing year round weather, beaches nearby, hiking, biking, diverse food options, San Diego and Los Angeles are both ~1 hour away so it's easy to explore some larger cities, excellent schools, safest city in the country (among the 100 most populous), and great jobs.
Best city to visit: San Francisco, California
I've visited San Francisco three times now in the past couple of years and I'm itching to go back. This place is stunningly beautiful and has amazing architecture for an American city, I haven't been anywhere else that comes close. The hills, the fog, the ocean, the parks, the food, the art, it's really a special place. It is grittier than some cities, about middle of the road in violent crime and high in property crime. The schools aren't as nice & the city has some real systemic issues, but goddamn if it isn't fun to visit. I actually took a very conservative friend on a trip there, and this is how it went:
We arrived in an east bay city in the early afternoon and took the BART into the city. We walked around downtown a little bit before making our way to Oracle Park, a bayside baseball stadium, to watch the Milwaukee Brewers play against the San Francisco Giants. The Giants weren't doing so well at the start, and went into the last inning down 2-5. They managed to hit a home run before getting any outs, 3-5. The second batter goes up and flies out. The third batter goes up, another home run. 4-5. The next three batters manage singles, one of them because the pitcher hit the batter, bases are loaded. The next batter goes up. The wind is cold and harsh. The stadium is electric. The hit is good. Silence while we watch the ball fly, and then we see it crest the edge of the field. The stadium erupted. The Giants won 8-5 on that grand slam. I never really understood why people liked baseball so much, but that made me get it.
The next day, we took a bus out to the western part of the city. We explored Golden Gate Park for a while, saw the buffalos, the Dutch windmills, some funny turtles, and then made out way down to the beach. We walked north to Lands End, where we went to a small museum about the old Cliff House and Sutro Baths, both of which are ruins now. We went down to the Sutro Baths ruins and then back up to the coastal trail. There were some pretty awesome views of the ocean and the golden gate bridge from there, it's very high up so you need to be careful when looking down at the waters below. On the other side, we gawked at mansions, had some amazing Russian food from a cheap local bakery, and some sushi. Before leaving the city, we walked down Lombard Street, got some dinner at Fisherman's Wharf, and walked along the Embarcadero.
All of that, and you know what - we didn't see any of the Mission District, didn't see the Palace of Fine Arts, Coit Tower, Chinatown, Union Square, the Castro, I could go on and on. My friend was blown away, the city was not what he was told it was. He's even talked about wanting to live there lol. Like I said, it has grittiness, not everywhere will feel safe. A good tour guide would go a long way. It's a special place, and I couldn't recommend visiting enough.