As people have said, look for schools, not cities. That being said, here are a couple of good ones that aren't in the middle of nowhere. Keep in mind however, that if you go to a big enough school, even if it's in the middle of nowhere, it won't matter because campus life is so big. I'm assuming you're going as an undergraduate, so this advice will be tailored to that.
My picks for city live + Education.
University of California, Los Angeles
University of California, Los Angeles, or simply "UCLA" is a pretty good school from an education standpoint. The girls tend to be pretty good looking, and you're right in LA. LA has fantastic weather all year 'round, and if you get tired of school life, you can always get into the LA club scene. If you're under 21, this can be harder, but if you're from Nigeria and you really lay on the accent you can make a fake drivers license in an inkjet printer and laminate it and most people won't know the difference. Make up some b.s. about how they don't have any of this fancy stuff in Africa and most times American bouncers will buy it, and if they don't they typically won't take your ID (which they probably would if it were an American fake driver's license) and just say 'we can't let you into the bar without a passport'. Another option is, most schools have Adobe Photoshop on their computers, take a scan of your passport, use Photoshop to switch a few of the numbers around so it says you're 21, and use a scan of your passport as ID. Again, this might not work 100% of the time but you can say you don't want to lose your passport and you don't have a driver's license. I haven't seen anyone use these techniques in a few years, so maybe bars have cracked down, but unlikely. You'll get a feel for things on campus, anywhere in the U.S..
Bottom line, UCLA has fantastic educational opportunities, tons of good looking chicks, a lot of stuff going on on campus, and the ability to go do things in Los Angeles if you get bored. I highly recommend joining a Fraternity, and at UCLA fraternities are relatively big. This isn't the SEC (the Southeastern Conference is an American Collegiate Athletic conference that includes big state universitys located in the Southeastern US, [University of Alabama, University of Mississippi, Texas A&M, University of Flordia, etc.] and are typically very fraternity oriented. I would not recommend any of these schools for you) but being in a fraternity has its benefits, including but not limited to immediate social proof, a more organized and structured social life, bros who have your back, and a generally fun college living experience. If you can afford it and like the people in a fraternity, I'd join. Definitely go through the recruitment process, which is often just a collection of parties.
New York University
New York University, or NYU is a good university located in downtown Manhattan, right in the heart of New York City. As far as New York goes, it's harder to be closer than the action than this. NYU is a good school, but from my friends who go their it seems to be a less cohesive campus than other places, and more just a collection of kids who live in New York whose full time jobs are to attend classes. Again, relatively hot girls and popping nightlife, but it will be cold in the winter and you might not be used to that, being from Africa and all. Also the city is so big and busy that it can be draining sometimes, but there is always something to do.
University of Miami, (Florida)
University of Miami (not to be confused with Miami University, which is in Oxford, Ohio) is a school that's probably a notch below UCLA and NYU, but still a good school. The pros of going to school in Miami, Florida are pretty obvious and apparent. First of all, Miami is georgeous, you're basically guarenteed to have beautiful weather all year round. Girls who go here tend to be pretty hot, and Miami is full of good looking girls. The only thing about Miami that I've seen is people tend to throw money around a bit, most kids have cars and are generally from well off families. Fraternities will also be big here, but you don't need to be in one to have a social life.
Boston University
Boston University or BU is a good school in, you guessed it, Boston, Massachusetts. Boston is a pretty great college town, although if you're under 21 they're killer on IDs. Much worse than New York, Miami, or Los Angeles. I don't know what it is but they're ruthless in that town. Beyond that, Boston is a pretty good city to live in. BU is a good school, but Harvard is just next door, along with Massachusetts Institute of Technology (MIT), and if you can get in at either of those institutions, from an educational standpoint, go there over BU every day of the week. BU may have hotter girls than either MIT or Harvard, but MIT and Harvard are much better schools. If you just want to live in Boston, Boston has the highest number of universities per capita of any city in the world. There are more than 100 universities in the greater Boston area, so you'll find something you like. Apart from the strict bar scene, you will also need to be cognizant of the weather there, as it's far worse in the winter than LA or Miami, and a little worse than New York.
At the end of the day, you will probably end up living in a coastal population hub, which in the United States is fairly expensive. New York will take the cake on Cost of Living expenses. From the context of someone living in Manhattan, if you were making $100k a year, to carry out a lifestyle of similar nature in Los Angeles you would only need to make $64,480 (I used Orange County for this comparison, which is probably more similar to Santa Monica than the only other LA option - Long Beach). In Miami you'd get six figures worth of New York for $49k, and in Boston it would cost $62k. Obviously you don't need $100k worth of New York as a college student, but
check out the cost of living calculator here to see roughly how far your money will go in each of the cities you're thinking of going.
Good luck and I hope you enjoy your time in the United States if you end up coming.