I'm wondering if I should take a (small) trip to somewhere in the UK during the term break... any recs?
When I was at Oxford, I likewise took advantage of those six-week breaks to do quite a bit of traveling, including a two-week trip to Scotland which I did on an extremely minimal budget and with everything I needed in one backpack. Please keep in mind that this was 2009 (I am. Old), and therefore almost fifteen years ago.
This itinerary included, more or less in this order, and with numerous day/side trips:
Isle of Lewis (in the Hebrides)
You can pick and choose depending on whether you want to see more cities, cultural sites, wilderness, etc. It might also depend on whether you can get around, as train strikes and other ongoing service disruptions can make it a headache to travel entirely by public transport. I don't know if they still have it, but I was able to buy a travel card for Scotland that covered almost all of my public-transit fares on train, bus, and ferry (that thing was worth its weight in gold). It is at least worth looking into some kind of weekly pass or seeing if there are discount travel options.
Likewise, I went up in the age before Airbnb, so I had to book regular B&Bs, which were generally affordable and run by nice people (one of them helpfully mailed my camera back to me after I accidentally left it in her room, and because once again, I am unbelievably old, I had to put cash in the post rather than just using PayPal to reimburse her for it). You will have more options, depending on how long you stay and where you want to go, but the nice thing about Scotland is that it is (well, usually) less expensive than England, and the North in general is cheaper.
If you don't want to go all the way to Scotland, I do recommend the North of England, which is gorgeous, huge, and empty. Northumbria, the Yorkshire Dales, Carlisle, Cumbria, Lindisfarne, Alnwick, etc are all doable by train from Oxford (once again, presuming that the train is uh, running), though it will take several hours and you will have to change services at least once. The Lake District is obviously gorgeous, though likewise touristy and more expensive at any time of year. That again will be somewhere to go if you feel like going out and hiking and enjoying the scenery, which may or may not be your bag. York is also lovely, if you haven't been there, and always worth a visit.
Wherever you go, make sure that you book train tickets in advance (as you've doubtless already learned that they scalp you on day-of) and check timetables. For example (though they may now offer it) when I went, some of the outlying Scottish isles/Hebrides did not have ferry service on Sundays, so if your itinerary relies on that, you might find yourself unavoidably delayed.
