Matt, Cambridge is one of the most interesting and beautiful places in Britain, with many historic buildings, principally the older university colleges.
The centre where most of the colleges are located is best thought of as an “A” shape with a spike at the top. If I were visiting for the first time, I’d start off at the foot of the left-hand leg of the “A” in Trumpington Street, walk up King’s Parade, Trinity Street, St John’s Street and Bridge Street to Magdalene Bridge (at the top of the spike), then back down the right hand leg - Sidney Street and St Andrew’s Street - and back to where I started via Downing Street. That route would give you a flavour of the city and the exteriors of many of the colleges. Depending on visiting times, as I went up the left-hand leg I’d go into as many of the bigger colleges as possible - particularly King’s with its chapel, Trinity and its Great Court and Library (where Isaac Newton studied), and St John’s and its Bridge of Sighs - but some of the smaller colleges such as Clare and Trinity Hall would also be worth worth a detour.
I’d also go down to the river and take a look at the views of the “Backs” of the colleges - possibly on a punt from the hirers at Magdalene Bridge - have a drink in the Eagle pub just off King’s Parade (where Watson and Crick set up the rounds as they investigated the structure of DNA), and queue for evensong in King’s Chapel, a world-famous daily cultural experience not to be missed even if you’re not religious.
That would be my tour. But I don’t live there any more. There are others on this forum who do who might have additional or contrary ideas. And who knows - you might bump into them!
I’m biassed, but I’d also recommend Peterhouse, down at the start of Hugh’s tour. It’s not the most famed of colleges — albeit the oldest — but the dining hall is very beautiful and architecturally very important; when the college had it redecorated for the 700th anniversary in 1984, in order to preserve it, they had it redone with wallpaper hand-blocked from the blocks created by William Morris for its re-decoration in the late 19th century, using inks created exactly as those used by William Morris on paper made to match the paper he used. When I was last taking friends round Cambridge, Peterhouse dining hall was the only one open to the public, though not in tour groups. The chapel has William Morris stained glass. The Deer Park and the Scholars’ Garden round the back, running behind the Fitzwilliam Museum, were always a haven without the hordes of tourists.
Old Court in Corpus Christi is the oldest residential building in Cambridge (14th century, I think) and perhaps worth a look … Milton had his rooms there. Apart from those I’d agree with Hugh, though I’d personally leave Trinity Hall off the list. Queens’ College and the Mathematical Bridge? Trinity library (The Wren Library) is a beautiful Christopher Wren building, with wood-carvings by Grinling Gibbons, and a life-size seated statue of Byron, carved at his time but kept in a cellar and apparently only installed in the place for which it was intended in the 1960s, so embarrassed were Trinity about his behaviour while there!
Go to Clowns Cafe on King’s Street. Have breakfast there one day.
Cambridge is great - it has one of the biggest Buddhist communities in the country and is also home to the headquarters of Windhorse publishing (a Buddhist publishing company). It is filled with lovely people and lots of bicycles.
Where will you be visiting in Scotland? I lived there for 25 years before moving to Colombia and still get very nostalgic. There’s a lot to see and do, particularly in Edinburgh, the West Coast and the Northern Highlands. The East Coast also has some nice spots. The main problem is time…
I was tempted to suggest, that you go by bike or kangaroo, but, I thought it sounded a tad juvenile, so I took an executive decision not to post!
I hope somebody on board is proud of me, for exhibiting a modicum of maturity.