If you like museums there's the free-to-enter Fitzwilliam Museum. There's also a dedicated Sightseeing bus tour, though it's freaking expensive IMO - you might be better off just making a list of the places on the route you find interesting and then getting a Dayrider to go there on the normal buses (Dayrider for the main Cambridge city area is £3.90, Dayrider Plus for the whole of Cambridgeshire is £6). If you want to venture outside of Cambridge proper, there's the Imperial War Museum at Duxford, where they have lots of older aeroplanes you can go inside and look at and stuff (if I recall correctly they even have a Concorde). They also have some boats and tanks and stuff too.
In terms of parks, Parker's Piece is a popular spot if the weather is nice, it's also apparently the birthplace of the modern game of football (they're going to put up a Subbuteo referee statue to celebrate this apparently).
I'm not much of a sightseer unfortunately but those are the things that I can think of off the top of my head.
