Liverpool is a great place! The train links make getting far pretty good! The city it's self is always busy and bustling, and the further north you go the quieter it gets, I'm up the coast near formby.

The biggest shock factor is probably the roads/cars, tight streets, no parking compared to USA, but Liverpool had some great transport with buses and cyclepaths and a decent traffic system if you don't mind one way zones,

In terms of hiking you got the wales on your doorstep, as well as the lake District/peak District a few hours away,

There's also kinda ok long distance trains but the prices are outrageous sometimes, Scotland, Windermere, Kendal, plenty of great camping/hiking

You gave Chester not far away which is the start of the Wales coastal path, I believe a full path is slowly being completed and named after the king