If it were me I would book a flight to London and book a hotel right in the city near the kings cross and paddington train stations - basically on a tube line that will get you there. See the city it is lovely and lots to do and safe for woman traveller alone. you can see museums, lots of theater, great restaurants. then you can take the train easily to various other places like a day trip to oxford other places like that. I go to London on business and always take time out for tourist activities often by myself and always enjoy the trip very much.
If you don't want the UK then try Australia / NZ. We just got back from 3 weeks there took a cruise around NZ lovely went to Melbourne and Adelaide. Both of those cities have excellent public transport no need for car. domestic flights in australia are easy and cheap. i thought melbourne was a lovely city very walkable things to see nice parks. same for adelaide people take the tram to the beach there.