What do you mean by "the university"? The university is spread across the city in various colleges.
OP, you can walk into some colleges and have a look around the grounds for free. We've been in both Emmanuel and Downing. Others you might need to pay a smalll charge to the porter.
There are some good suggestions on here. I'd definitely book a walking tour, they are great if you haven't been to Cambridge before. You can spot stuff that you can return to later on your own for a proper look eg we visited the Eagle pub which they always mention on the tour.
Bould Brothers for coffee (there are two). Aromi is good too.
Botanical Gardens are nice for a wander (I like the greenhouses), there is a small charge.
Punting is lovely, with a guide, although not sure I'd enjoy it in March, we went in summer and it was a warm sunny day.
The walk from the station is fine if you are used to walking everywhere. Those who drive door to door, or who are unfit/elderly would probably complain.
Check if there are other museums open. I think the Sedgewick museum of earth sciences is open on a Monday. It has a nice museum smell and doesn't seem to get very busy so is nice for a wander around in peace if you like that sort of thing.