Winter in the UK with no car

Bath, Glastonbury, Edinburgh, Cambridge are good places to visit in UK during January. Also Sheffield England is good. The town has a vibrant university.

I'm actually in Aberystwyth which is about the worst for connections, but I'll be in London at the beginning and end of my break, so that will make access easier. I do like the idea of going up to Durham and Edinburgh but I wasn't sure about how that would be weather-wise in the winter.

I'm also interested in Cambridge--is there much that's accessible in the area around it?

If you have five weeks free and using the train frequently, In case you weren't aware, there is a 16-25 Railcard and a 26-30 Railcard, valid for 12 months, once bought these will give you one-third discount off most Rail fares in Great Britain, including walk-up tickets, you can also have the Railcard discount added to a London Oystercard.

There is a mon-fri minimum fare before 10am.

https://www.16-25railcard.co.uk/

I am actually too old to qualify for any of those (postgrad), which is such a shame!

What kind of museums?

Any particular periods of history?

The youth rail cards are an excellent idea. UK rail fares are among the very highest in Europe on a per-mile basis. There are fast trains to whisk you rapidly between major cities (I think roughly 2 hours to York and 4.5 - 5+ hours to Edinburgh), but you pay (in effect) by the mile rather than by the hour, so those can be very pricey trips if you buy an "Anytime" ticket. Even at 2/3 of the full Anytime fare, tickets can be painfully expensive. Advance fares, where available, may beat the youth discount handily, but those Advance tickets are quantity-limited. It's worth exploring fares during your travel period on nationalrail.co.uk to see what savings might still be available. The big savings will probably be on the longest trips.

Edited to add: I see that the youth cards are not something you can use, but you may still be able to take advantage of the variation in ticket prices over time. Compare current London-York prices for travel today (Wed. UK time) to those for January 15th (random date chosen by me). Huge difference, right? Some fares will vary more than others, so you can fiddle with the timing of your various trips to position the most-variable travel segments later within your free period.

Another wrinkle is that fares are sometimes lower if you split a long-distance ticket into two or three segments.

In addition to Edinburgh, Glasgow has a lot of good museums. However, it tends to be a bit wetter than Edinburgh, I think, and that's saying something.

There are some lovely small towns accessible from Cambridge (probably by bus), but I'm not sure what they'd be like in the winter. That doesn't seem the best time of year for places like Lavenham and Bury St. Edmunds.

Not horribly far from Cambridge but too time-consuming by rail to be a day-trip is Bletchley Park, the WWII code-breaking center. It's a very interesting visit and can just about a full day even if you don't go to the nearby computing museum. I day-tripped to Bletchley Park while staying in Coventry because I wanted to see the modern cathedral.

Oxford is another picturesque university town with a pair of fabulous museums.

There is tons to do in London, and for a December/January trip I'd spend a lot of my time there unless I planned to hop on a plane and spend a good chunk of time in a warmer spot (southern Spain or Morocco, perhaps). Damp, chilly weather would not be much of an impediment to enjoying London, but do read lodging reviews to be sure you don't reserve a place with a bunch of complaints about inadequate heating in the winter.

If the prospect of heading south for part of your free time sounds enticing, check skyscanner.com now to see whether any bargain flights remain available. I assume your best options will be for the period after New Year's.

Mature students are also eligible for the 16-25 Railcard regardless of the ages in the name:

A mature student?

To be eligible as a mature student and buy a 1-year Railcard, you will need:

To be attending a recognised college or university, for over 15 hours
a week, at least 20 weeks a year. Unfortunately, Open University,
distance learning and part-time courses do not qualify. To have the
mature student section of the 16-25 Railcard application form
completed by your College or University. Have an NUS card or
College/University photocard as proof of identity.

https://www.16-25railcard.co.uk/using-your-railcard/are-you-eligible/

Thank you everyone for your thoughts, and especially thank you to Nigel for pointing out that there's an exception for mature students!

Firstly, in case you missed it last Friday, the Cambrian Line was shown on Channel 5 in the series - World’s Most Scenic Railway Journeys. It did not show the branch going from Dovey Junction to Aberystwyth but did show the Pwllheli to Shrewsbury line - I suggest you watch it via the My5 catch up via the internet:>https://www.channel5.com/show/worlds-most-scenic-railway-journeys/

I take it that you are aware that for longer distance rail journeys, pre-booking specific trains gets you lower prices. These normally get loaded around 11 weeks ahead but even the day before travel will often show lower prices than pay on the day.

In the event that you travel to/from Edinburgh, then you would need to go from Aberystwyth to Shrewsbury (change) and then to Crewe (change) or Manchester (change). You do not go via London - although you could do that in one direction - but it is much longer. On some journeys, it works out cheaper to split the ticket - often at the place where you change trains/company. This website is pretty good at advising you of the best prices/route options:>https://www.traintickets.com
(If you do split the tickets, ask staff that you wish to retain the first leg(s) tickets at any barrier as proof of travel. This is important should any early leg be delayed meaning you miss a connection and have to travel on a later service).

The Welsh bus routes that begin with a T are free at weekends. So, you could, for example, go all the way to Cardiff & back for free. (Please note that over some of the Christmas period that if using the trains, Cardiff Central’s mainline services are probably not running as they do final testing before starting an electric Inter City Express service to London. Other rail routes may also be affected by engineering work over the Christmas period). https://www.trawscymru.info/routes/
https://www.visitcardiff.com

If you have some spare time, consider taking a local bus down the coast to Aberaeron. https://www.cardigan-bay.com/aberaeron-cardigan-bay/

In England, Shrewsbury is worth a look as is Birmingham - Christmas Market currently on >https://www.thebfcm.co.uk
Chester is also worth seeing and a night or 2 here could be combined with a day trip to Liverpool.

Flights on discount carriers are very inexpensive. A young friend of mine goes all over Europe on weekends from the UK on a strict budget. Uses AirBnB., shared with classmates.

If you haven't already discovered it, the master guide to train travel in the UK (and elsewhere) is this site:

www.seat61.com