The Cathedral in Worcester is very interesting, I think I've been to Coughton Court too but it was a long time ago!
The Royal Worcester Porcelain museum is interesting if you like that sort of thing..
250 years of stories told through the largest collection of Worcester porcelain in the world, where it was made. Museum of Royal Worcester.
www.museumofroyalworcester.org
It was possible to have a tour of the factory many years ago which was great to watch how things were made and see staff hand painting stuff but it looks like the factory building is an event space now - I guess because they are now part of the Portmeirion Group, which I didn't know til just now.
I can't help you with the pubs I'm afraid