Wells is very nice and there is also Glastonbury, with the Tor and Street, which has a big shopping village.
I don't use local pubs, so can't advise, but you must eat at Yoji's, a Japanese restaurant in St James Street. You will also find some good places to eat on the Boullevard, which is at the bottom of the High Street.
The pier was completely rebuilt last year, after a fire, so has got to be good for the kids, and if you are lucky, the new Italian restaurant on the sea front will be open.
If you like a bit of fresh air, at the far end of Weston, down the old toll road (part of my regular training ride) you will find Sand Bay (The New Castle at the end of the toll road is a nice place to eat). Drive to the very end of Sand Bay and there is a headland owned by the National Trust. It's a good place to clear the cobwebs, as you are right on the Bristol Channel.
Alternatively, you can park just below the New Castle, near The Commodore (bit of a so so reputation these days, but popular with the older residents). From the car park you can walk up into Worlebury Woods (another regular training ride). There's an natural play area in there, and plenty of walking, including a trail to a pile of old stones that was apparently an iron age fort!
Bristol is only 25 minutes down the road, and there is a ton of stuff to do there, including a massive interactive science exhibition, The Great Western and also The Shed, which is the Bristol industrial museum that has recently been rebuilt.
Between the shed and the great western is a little outdoor cafe called The Bristol Buttery. Treat yourself to one of their bacon sandwiches. In the opposite direction, across the small swing bridge, is Mud Dock, bike shop and cafe.
I'm sure there's loads more, but as a local you tend not to think about places to visit.
I hope that helps.