Best thing to do in Chongqing

Hello
I am travelling to CQ China late November for two weeks. Is there any particular attractions that are worth to see? In particular, any adventure or rare things to see and do?

I am then going towards beijng or shanghai for a week each. Is there any cheap but good quality hotels? How about things to do and see? I What is the best way to travel to these cities from CQ - train, bus?

And as I am vegeterian and very particular about meat touching food or being cooked in same pot, will food be available... ( I know, weird)