I recommend going to Cambridge on a weekday, that way you can avoid the huge crowds of tourists that flood the city every weekend. Cambridge is a small town, the centre of which is dominated by university and college buildings, and their beautiful old inner courtyards. "Colleges" are part of the university, but each is like its own mini castle with its own gardens and distinct architecture. There is a lot to see, and you won't even be able to see all of it in one afternoon.
Don't be afraid to wander into any and all of the colleges. While the town may seem closed off at first, the only places you need to buy tickets for are King's College, King's College Chapel, and Trinity College. And for those, you can go in for free if someone affiliated with Cambridge takes you along with them. The rest of the colleges are open to visitors.
I highly recommend going inside King's College Chapel, it's grandeur is completely disproportionate to the size of Cambridge itself. It's worth coming to the town just to go inside the chapel.
King's College Chapel. Photo: Olga Zeveleva
When it comes to colleges, King's College and Trinity are two of the most popular tourist destinations, but don't miss St. John's College, which is close by and open to visitors most of the time. Go to the back of St. John's and cross the Bridge of Sighs, you'll never forget the shapes of the shadows it casts or the tranquility of the River Cam beneath it.
Bridge of Sighs, St. John's College Cambridge. Photo: Olga Zeveleva
Even if you don't make it into the courtyard of Trinity College, go to their famous library - the Wren Library. It's open for tourists Monday to Friday between 12 and 2.00 PM, and during full term you can come by on Saturdays between 10.30 AM and 12.30 PM. It's around the back of Trinity College near the river - don't go in through the main entrance, instead go to the side gate on Garret Hostel Lane. Inside you'll see oddities like a lock of Isaac Newton's hair and some of the first Winnie the Pooh books.
For breathtaking gardens that change every season, visit Newnham College. Newnham is open to visitors, and, unlike most of the colleges, you can walk, lie around, and picnic on the grass. Enjoy the flowers, the beautiful and somehow delicate red brick buildings, and look out across the football pitch to the white house where Sylvia Plath lived when she was at Newnham. The intricate gate leading into Newnham casts lovely shadows too - do make sure you watch the shadows when in Cambridge.
For feeling like you're in an Italian fortress, go to Jesus College and just keep going through the mazes of their courtyards until you get lost.Murray Edwards College offers some insane brutalist architecture, so don't miss it if you really like concrete. For the most manicured grass you'll ever see, go to Pembroke College, which is a lovely small college right in the centre of town that you won't want to miss.
Pembroke College. Photo: Olga Zeveleva
The Orchard Tea Room is a 25-30 minute walk into the fields along the river, where Virginia Woolf and Russel and Keynes used to go for long strolls. In the opposite direction along the river if you're up for a 45 minute walk outside the city centre, you'll find a pub called The Plough in a tiny village called Fen Ditton (just outside Cambridge), lovely for sitting outside overlooking the water on a sunny day, and it's a beautiful walk. You'll see lots of house boats and lively river/riverside activities.
Go to the Cambridge Brew House for the widest variety of local ales (they brew them there). The Mill pub on the river is the most famous pub in town, and The Anchor is where Pink Floyd used to hang out. For wine, go to the Cambridge Merchants wine bar on Bridge Street.
Walk to Fen Ditton. Photo: Olga Zeveleva
A more conventional answer than that of Olga would note that visitors should respect signs which state whether a college is open or closed (or ask if it is not clear)!
Off the beaten track, one might have a coffee at Indigo's hanging out with the students, admire the Mathematical bridge from Silver Street (or walk across if Queens' is open), visit Charles Darwin's room at Christs', Pepys Library at Magdalene and Clare gardens if the weather is good