Best England destinations by rail in Autumn

You are well placed in Liverpool for visiting the Lake District and North Wales. Some possible destinations: Chester, York, Durham, Caernavon, Hadrian’s wall, England’s northeast coast - Lindesfarne Island, Bamborough castle. Just bear in mind that weather and daylight hours in fall/ winter can have a big impact on what you can see and do, so try and get the outside things done first - Hadrian’s wall, the northeast coast.
Consider a weekend trip to Scotland - Glasgow for example.

cool architecture

Well I suggest a weekend in Ironbridge, to well, see the Iron Bridge - the first iron structure and check out the Museums of the Gorge.

Agree with Leslie.

York and Durham are great need 3 nights in York and you have been to Durham.
Winchester is a favorite as is Salisbury.
Cornwall and Devon are great, but hard to do on a train. Consider a Rabbies Tour. We did it from London and it was inexpensive and great.

Also, North Wales has Conwy Castle and more.
South Wales has Cardiff (castle and the Museum of Welsh Life), also, Tenby and St. Davids.
Lots of castles in Wales.

That is very exciting, and you will be well located in Liverpool for taking trips by train. Some nearby places I personally have enjoyed:

-Manchester (very easy to get to, loads to see here including the Science and Industry Museum, which I really like)
-The Lake District- this is a very big area- if you are going by train you can easily get to Kendal and then either take the branch line to Windemere or take one of the buses; there are also boats you can take on some of the lakes
-The northeast- Northumbria is really beautiful, and Newcastle is easy to get to on the train and a good base
-Yorkshire- a very very big area, York is lovely and then you also have the dales for scenery- and I particularly like the coast up by Whitby
-The Peak District- you can base yourself in Sheffield and visit places like Stanage Edge on public transport (train to Hathersage)
-You're also extremely close to North Wales- you have the nice coast (e.g. Llandudno) as well as Snowdonia (for mountain scenery) and Caernarfon

As mentioned above, just remember that as we get into autumn, particularly after the clocks change at the end of October, sunset is quite early.

Good luck with your exchange programme.

Head south to Bath - ancient Romans in Britain had thermal baths there (which are still an historical sight), and modern English developed it further. Soak in the mineral waters, have a posh Afternoon Tea in the fancy Pump Room, and there’s more to see in town, as well.

Lesley's idea to get as much as possible done outside early is a great idea. Bath would be a great place to visit when the days are shorter and cooler. We loved tea at the Cresent in Bath.

Liverpool has a comprehensive local train network that covers the city and a wide surrounding area.- Merseyrail Rail. The bus network is also good.
You can get to Chester in about an hour and Port Sunlight in about 20 minutes.

https://www.visitbritain.com/en/destinations/england/chester
https://portsunlightvillage.com/

Across the Mersey is the Wirral. It’s a real mix, some of the poorest areas in the country and some of the wealthiest.
Birkenhead, which tends towards the poorer end, has Hamilton Square, a beautiful Georgian square and Birkenhead Park, the inspiration for New York’s Central Park.

I have a real soft spot for Parkgate on the Wirral ( if you are local the k is silent). It’s a pretty village with great view towards Wales over the Dee estuary. It has a really interesting history. Before it silted up it was a main port for people travelling from Ireland. Great for birdwatching as well.
https://en.wikipedia.org/wiki/Parkgate,_Cheshire