For fine dining (and of course higher prices) you could look at somewher like the 2 Michelin starred Midsummer House, which has a lovely position on the River Cam. You could also try Alimentum, which has one Michelin star and is also highly rated. Neither is cheap, of course - a 3 course offer at Alimentum is about £40. For more high end restaurant ideas click here.
If you are looking for something more within budget, the Oak Bistro is very well thought of - small but very good food. As always, Tripadvisor can offer you plenty of opinions (some conflicting, admittedly). According to them, the most highly rated restaurant in Cambridge is an Italian, Piccolo Mondo. In fact Cambridge is well known for its international mix of cuisines and it is a good idea to try putting 'cambridge italian' (or Indian, or whatever cuisine you feel like trying) in a search engine to get a wider range of choices.
Finally, if you want to try the student experience, you could go for one of the many budget restaurants available.