As AI T mentioned, there's a mix. We tended to go to The Smugglers in Morecambe, because it was very close to my flat of the time and had an in-house ukulele band. Which is brilliant, if you like ukulele bands and small, very local, pubs. You will soon get to know, through local talk, which ones to avoid.
Lancaster has a bigger selection, but as a university city it can be fairly rambunctious. Not to the extent of Birmingham, Leeds or Preston, but still up there. I remember walking home after missing the last bus and getting excitedly leaped on by a student who mistook me for a member of his pub crawl team, but generally it's all rather brilliant.
There are plenty of museums and a steady night life, some people will regularly go up to Scotland for the weekend. I love Edinburgh,
If you're keen on castles, Lancaster Castle is quite nice. Similarly if you can get down to London I'd recommend a trip around Lambeth Palace, I'm not sure if you'll get quite the same treatment as I did on my induction day but it really is rather splendid. Beautiful rooms, and a whole lot of history. I think as a non-NCI staff member you'd probably have to pre-book yourself on a guided tour, and I think it's something like £15 each, but if you like that sort of thing it is lovely. Plus the carpets are really nice. Really nice. Like walking on clouds.
I'll second coming down to the glorious South East for a visit to Canterbury (not that I'm biased). Probably best to make a weekend of it, the 3+ hour trip is a little long on an often crowded train, but definitely worth it.
Really it depends on the sort of things you enjoy, I'm touching 30 and tend to hang around with people in the 40+ range nowadays, so my idea of fun may be out of touch

.