Hank, While you're in London you can get a Coach (Bus) Tour that will show you Stonehenge and Bath and The Cotswold Villages - very pretty and very old.
Leeds Castle (not in Leeds, close to London).
Stonehenge is not an overnight stop - remember what I said about distances in the UK being smaller?
If you need to fill a gap take the Train (or Bus) to York.
Very old - lots of History and a Museum that will take you back 150 years walking the streets of Victorian England. Go into Old Shops and see people dressed in the 19th Century style. Fascinating. York Minster. Massive Railway Museum. Google them!
Its a Tourist Hotspot for good reason. I love it !
Remember Chester and Conway are just a short distance from Liverpool by Train. You can have a full day at each one and return to Liverpool in the evening.
They'll both be much more expensive than sleeping in Liverpool.