I am assuming you've never been there before? Suggestions:
Fitzwilliam museum - if you like museums!
King's College Chapel - if you've never been to Cambridge you really ought to pop in and see the chapel.
Walking along the Backs (basically walking along the river) - (if it's a nice day) really pretty and generally nice to do
Wandering in and out of colleges (some might be shut, and some might charge). Most of the town centre ones are really beautiful.
Kettle's Yard - if you are more into 20th century art, this is a really nice place to go - based in an artist's house. website
The Botanic Garden is very nice, although a bit out of the town centre here
In terms of shopping, if you want all the usual high street shops, go to the Grafton Centre (about 10 mins from the town centre on foot). If you want high street shops plus independent shops, wander round the town centre.
You can go on a red double decker tour, but to be honest I'd save your cash and just wander round! You can also download an audio tour if you've got an iPod! here
Don't know about parking I'm afraid! THere is a park-and-ride which might be worth investigating.
This website is good for maps, info etc.
Enjoy your trip!