Half term short break suggestions

[Missedmytoe]

After some inspriation

Looking for somewhere for me & 1 DC to go for a few days (3 nights max).
We have the following requirements:
Must be accessible by rail
Must have budget accommodation
Must be able to walk around (and ideally walk from station to accommodation)
Museum(s), Art Gallery(s), Historic House(s), Cultural & Historical interest points - e.g. Castles, etc.
Decent eateries & tea shops

We were going to try Manchester but everywhere I've looked at is either already booked or too expensive.
Thinking about maybe York.
We're in the SE so would prefer to travel further afield/north of London
We won't have access to a car

Try the youth hostel association the city centre ones are usually ensuite and similar to a budget hotel.can either self cater or have breakfast/evening meals.

Liverpool, Manchester, York all good for museums, train stations and walkable.