I live in Oxford, but can't add to the suggestions given. All I know is that the open-topped bus is very popular. I have been trying to think of hidden gems, but gone blank. For the locals, town and gown are very separate, and I am ashamed to say I haven't visited the colleges for many years. My favourites were Magdalen for the deer park and Christchurch meadows.
It may not be available yet, but I hear that the weather is going to get much warmer, so how about taking a punt on the river? If you don't feel that energetic, I think you can have an escort to do the hard work, or you could take a steamer trip.
I hope you have a great time.