I travel to Chongqing a lot. It's one of the more interesting cities in China.
Visually it's unique. Built into mountains and hills, every road surface is on an incline. It's a nice city to *look* at; there are parts just like Cloud City from Empire Strikes Back. The geography results in some bizarre buildings, e.g., the lobby of your hotel will be on the 23rd floor, the parkade on the 13th, and two major roads passing by floors 1 and 11.
It's a sprawling city. Make sure your school campus isn't too isolated, or you'll be traveling an hour and a half (one way) to get anywhere interesting. Subway is convenient, but sometimes only takes you closer to where you want to go, not all the way there. Cabs, buses and 电瓶车 are other options. On the plus side, taxicabs are cheap compared with other large cities. Due to the mountains, it's not really a city for bicycles.
Chongqing people are great. Being on a college campus you'll also have a nice cross-section of foreigners and Chinese people from other parts of the country. The women in Chongqing are beautiful--even in they have a reputation throughout Sichuan for being crazy.
If you like spicy, the food is fantastic. It's even better than Chengdu (where I live), and that's saying a lot.
On the downside, young people don't go or hang out the same way they do in Beijing/Shanghai or even Chengdu/Kunming. There are a few places with live music--坚果/Nuts and 马格/Mug Bar--but far less than the other cities I mentioned. If you like clubbing, KTV, or going out for hotpot, you'll be fine.
Chongqing people do not speak standard Mandarin. Hopefully your teachers have standard accents -- I would check on this before choosing the school. Also, 重庆话 will sound incomprehensible until your Chinese gets together. I'm not suggesting you can't learn Mandarin in Chongqing. Of course you can, but if you want to speak with a standard accent you'll need (1) friends from Northern China; (2) access to standard Chinese audio--like Popup Chinese; and (3) pay close attention to phonetics. Don't pronounce bāi as bēi, shì as sì, etc.
If you do move to Chongqing, come to Chengdu and visit. Chengdu is a big city with a completely different vibe, and only two hours away by high-speed train. Tickets are cheap, at less than 100RMB.
EDIT: Chengdu itself is an option; 四川大学 has a well-known Mandarin program. The city is more cosmopolitan and laid-back than Chongqing, which can be good or bad, depending on what you're looking for. Note that Chengdu people do not speak standard Mandarin, either, so what I wrote about Chongqing also applies. Due to geography, you have more choices for transportation, and the city is less spread out generally.
Good luck, whatever you decide!