I used to live in Wem so I shall give you the benefit of my years of carefully accrued knowledge!
Wem itself is a fairly small market town but Wem Town Hall has regular live music, theatre, flicks in the sticks etc and it's worth a look on their website. There's a swimming pool and a reasonable choice of little high street shops plus a decent Co-op supermarket. The walk from the campsite (I assume you are staying at Lower Lacon Caravan Park) is a proper footpath into town and wouldn't take more than 10 minutes at most. The Old Rectory is really nice for meals as well.
There are trains about every two hours (much quicker and more reliable than the buses) into Shrewsbury, it's a 15min train ride. Shrewsbury itself is probably my favourite place and well worth a visit, although it is fairly hilly it is not unmanageable. There are lots of lovely little individual shops as well as your big high street names and the architecture is gorgeous.
Theatre Severn has a lot on and is worth a visit to the coffee shop for the lovely views over the river. Visit Shrewsbury is useful website too. I highly recommend going down to the park (also know as the Quarry or the Dingle) because it is lovely to mooch along the river banks - there are proper wide tarmaced paths - and the flowers in the central garden are stunning. There are also a lot of nice places for eating/coffee, my personal favourites are The Old Market Hall, The Armourey, The Bellstone and The Lion and pheasant.
Depending on when you go the Shrewsbury Flower Show is worth a days visit and they have fantastic fireworks in the evening (which are free to watch if you stand on the opposite river bank!) Or there's Shrewsbury Castle to visit.
Another really lovely town is Ludlow. It's about 40 mins by train from Wem through the most beautiful countryside, lots of beautiful old buildings again, fab little shops, cafes and restuarants and a 'proper' market on Fridays and Saturdays. Ludlow Castle is worth a wander round too, and in September is the Ludlow Food Festival which is held in the castle grounds and throughout the town and is thoroughly brilliant.
Just looked back and seen how much I've written but hopefully will be of some use. Everything I've mentioned is wheel chair accessible, one thing to bear in mind though is that the public transport from Wem isn't as often as one would like so make sure you don't miss the train/bus as it's normally a while to the next one! Feel free to PM me if there's anything else you want to know 