Where should a solo female traveler spend 2 nights outside London?

Anywhere in the UK is safe to go, so long as you don't get drunk and walk around in the early hours of the morning.

York is one possibility, easily reachable by train from London and compact enough to see in your timescale.

Canterbury with a day trip to Whitstable or Dover would be a shorter journey.

Brighton has the Pavilion for history and The Lanes to explore for antiques and quirky shopping and is surrounded by the South Downs if you want to explore the countryside.

Lewes - spend a day exploring the castle and its history and a day in the pretty nearby villages of Alfriston and Jevington.

Look at the National Trust website and see if any of their properties interest you and plan a trip around this.

Manchester, Liverpool and Leeds all have good selections of museums and galleries, whilst not being on the obvious tourist trail, they would have plenty to occupy you.

Two nights is really only one day wherever you choose.

I never rent cars so relying on the trains is second nature. My favorite city outside of London is York and I spent two nights at a B&B on my own. I absolutely loved it.

Oxford is another possibility. Not far from London and fits your interests.
Use the train planner of the National Rail for connections and advance buying of tickets.

Another option would be Chester, so much to see and do.

Or Cambridge with a side trip to the Cathedral at Ely.

Or Norwich, another cathedral and a castle.

I would feel safe in every city although I would possibly avoid Dover if I was on my own.

Given that you like scenery my suggestions are all towns or small cities where the surrounding countryside is more accessible.

Cheltenham is a nice regency spa town like Bath but not as touristy. Easy access into the Cotswolds and Gloucester Cathedral is close by which is very impressive.

You could head towards the south coast. Bournemouth has lovely long beaches and great walking to places like Hengitsbury Head overlooking Christchurch harbour, the upmarket Sandbanks (the most expensive area of real estate in the country) or take a trip over to Brownsea Island for great bird wildlife or the ferry over to lovely studland bay. This isn't such a historic area but you could combine with a visit to Dorchester which is a short train ride and the home of Thomas Hardy.

You could even take the train to the Isle of white which has lovely scenery and old Victorian charm.

Claudette, you are getting lots of recommendations and that should reinforce how safe it is for you to go wherever you like in England on your own. Peruse travel books and websites to see what interests you and then make your lodging reservations. I'm going on my own in April and can't wait.

Thank you all for the recommendations and reassurance of safety. I promise not to get drunk and stagger home from the pub in the middle of the night lol!