I lived in Cambridge for several years & have visited Liverpool quite a few times.
I like both places; they (obviously) feel very different – Liverpool is a much larger place with much more bar/club nightlife.
Cambridge is a small city, but there’s plenty to see & do for a weekend. The nightlife is a bit rubbish in Cambridge, but there’s tons of decent pubs.
Regarding Cambridge:
The Premier Inn on Newmarket Rd is well placed for a short walk into the centre of town, although the road it’s on is a bit rubbish and there’s limited parking (should be OK at the weekend).
There’s another Premier Inn on the north side of Cambridge just off the A14. This isn’t in a very nice area & you’ll get stung for cab journies, so I’d avoid if possible.
The Travel Lodge in the centre of town quite often has good deals – parking is bit pricey (but then it is all over Cambridge) and it’s a decent stroll into town, but a perfectly fine place to stay.
If you like aeronautical stuff – Duxford is only 20 mins from Cambridge & will easily fill a day.