Well it depends on what you are into and what you like.
While staying in the city I would certainly recommend a walk through Jiefangbei, visting of "Luohan si"(budhist temple in Jiefangbei where you can see a lot of arhats) and "Laojundong"- taoist temple in "nanshan"(south mouintain where you can enjoy one of the best view of Chongqing while drinking tea).
If you want to travel out of the town so there are no limits ...
If you are more specific about what you are into so I can make better recommendation

why not check out the lovely changjiang

You can take bullet trains to Enshi Canyon, Mt. Emei, Mt Leshan, Chengdu, then bus to Three Natural Bridges as well as to Chisui Danxia Landform.

You can also take overnight trains to a lot of awesome places, do your research, use http://www.travelchinaguide.com/china-trains/railway-map.htm

and

http://www.travelchinaguide.com/china-trains/