I have spent time in a few U.S. cities that I felt were more walkable and European, with acceptable or even excellent public transportation to match. Naturally the United States is going to lag far far behind European cities in terms of livability simply due to the fact that the proceeds from our relatively low tax rates mostly go to the permanent wars that prop up the arms industry and welfare programs to subsidize GloboHomo corporations. For reference, the most livable city I have lived in was Munich, so that's what I'm comparing these to.
Best:
New York - lived here. Excellent public transportation. So they are not as good as German trains. There are crazy assholes on them and bums taking a shit. But... that's the New World, buddy. The trains go, and they usually go on time. Can walk most places and where you can't walk, you can take a train. NYC has the best public transportation in the US hands down.
Boston - lived here. Also has excellent public transpo. Fewer crazies than New York. But also fewer trains. For all its batshit liberal insanity, Boston is actually not a bad city to live in if you don't mind the cold or the high cost of living. The benefit of Boston is it's small. You can walk across the city in a couple of hours.
Decent:
Seattle - visited for a week. City has public transpo that is okay. The city proper, at least, is easy to get around and pretty nice and well-maintained. The tradeoff is it's full of drug addicts and aggressive bums. There are hot chicks, though.
San Francisco - lived here (or close enough). The city proper has public transportation and it runs. It is also one of the few cities on this list that was planned to be a large city. Irishman-turned-Spaniard Jasper O'Farrell (namesake of O'Farrell street) planned the city as a grid in 1848 to maximize the living space for people coming from the East Coast during the Gold Rush. Large portions of the then-SF Bay were filled in with sunken ships and the city built on top of them. The city proper is a relatively small peninsula (7 miles by 7 miles) so many places are in walking distance if you're up for it. It is the opposite of a sprawl. Of course, the stereotypes about the ridiculous cost of living, homeless people shitting on the streets, and general liberal douchebaggery are all true.
New Orleans - visited here for a week. Not much public transportation to speak of, but the heart of the city is what - almost 400 years old I think? - and thus built before automobiles, so it is fairly easy to get around. Cost of living is also ridiculously low. There are obviously extreme urban planning issues regarding the levees as we saw in Hurricane Katrina. But during my stay there, I found it a pretty livable city. The people were nice and the food was good, too.
Worst:
Los Angeles - lived here. No surprises. Los Angeles was built by the auto industry. A hundred years ago, when the city was first beginning to flourish, they tried planning a vast network of subways and suburban trains that was supposed to rival New York's. The car lobbyists killed it. LA is the sprawl of sprawls. Everywhere you go, there is traffic. Everything you want to do, you will wait in line for. There is no way around and there are no shortcuts. You gotta sit there sucking in fumes with the rest of 'em. There is SOME public transportation runnning through the "core" or neighborhoods adjacent to downtown, some of it running as far north as Pasadena and as far south as Redondo. Those trains do run on time and frequently enough to be useful. But if you don't live pretty much next-door to the train station it's a moot point, as you will sit in traffic just to get to the train. I also got threatened with stabbing multiple times on the Green Line, which was fun. Oh and the busses in LA are pretty extensive too, but again, a homeless dude jerked off in the seat behind me at least once a month during the year I took the bus to work, so... Basically do not live in LA unless you are within a three-mile radius of your job or you manage to somehow snag a place literally next to your train station. And even then, bring goggles.
San Diego - lived here for many years. Another car city. Fun place to live but horrible layout unless you live in the North Park/Normal Heights/Hillcrest area, which is walkable and a pretty great area in terms of location and things to do. But Hillcrest is full of gays. So it goes.
Did not live in or visit, but have heard good things about...
Boise
Portland
Chicago