Rental market is buoyant atm, properties go pretty quickly. Taunton has way more options and isn't far from welly, though you would have to drive. If it absolutely must be welly then as a rule the South side of town has the better neighbourhoods.
Town it's self is pretty small so likelyhood is you will end up buying in one of the villages (milverton/nynehead/Bradford on tone) a little way out. Some biggish housing estates on the edge of town, not really sure what these are like though.
How old is DS?
There is a small cinema in town which sells alcohol and is pretty cheap. But only one screen so viewing times can be a little odd. They do show plays etc from the national theater.
Other than that not much going on in town. The rugby club is good and there are quite a few other groups around.
There is a community orchard you can go and pick fruit at (not great this time of year obv)
Some very good takeaways in town. The Indian resteraunt is exceptionally good. Would recommend the Dolphin pub for both the food and the atmosphere.
The whitehorse at Bradford on tone does a cracking Sunday lunch, but book.
If you absolutely want a night out in Taunton then the taxi is about £17 to £25 to get between the two. Bristol is only a half hour away from Taunton by train and the car parking at the station is only £6 a day so lots of options there.
Lots of walking opportunities. Either straight from town heading towards the monument or around the basins. You can drive out to Triscombe/Crowcombe and walk the Quantocks. Exmoor/Dartmoor obviously not far away either. The orchards at sheppys cider at free to walk around and the resteraunt there does a decent meal (plus sells their farmhouse cider with 0 preservatives in... Top stuff)
The Runwell farm shop is very good and a decent cafe there as well.
There is a steam line that runs out to the coast that isn't horribly priced (although not from Wellington)
Dunster and the castle are lovely.
Feel free to PM if you need anything else.