Premier Inn is on J34. If you don't already know, the roads around there are currently a building site! They are building a new road that will hopefully make the trip from the M6 to the Globe about 7 minutes, instead of the 45 it can take at the moment, so plan for that one.
You have a Brewers Fayre on site.
Centre of town is a good mile and a half down the main road and there is nothing on your way, so you may want a taxi.
Lancaster is quite historic and has quite a few cask taverns and plenty of bars for the Saturday night brigade with the short skirts etc.
If you are with family you will probably want the former and we all have our favourites...
I would certainly try the 3 Mariners (oldest pub in Lancaster)
The Sun
The Water Witch (on the canal if you go in daylight)
The Merchants
The Robert Gillow (often has live acoustic)
Ring of Bells (sometimes has a band on)
John O'Gaunt
The Study Room
Wagon & Horses and the George & Dragon (heading down the quayside)
There's also 2 Wetherspoons and a Yates
The "Pub" has rock music
Not generally too much in Live entertainment apart from at the Globe at 3pm
That lot should keep you busy!