Walnutshell we've recently been house and area hunting so we do know quite about about the areas, including schools, house prices, transport links etc, but we particularly looked in Exeter itself and up to about 5 miles around, not further out, as we commute in by bike.
I can tell you more about the areas if you CAT me. am a bit reluctant to give out too many details on a website. also the areas we ruled out might be where other mumsnetters live! for example we ruled out buying in one area because it has a failing secondary school at the moment, though we liked it in other ways (around the university). But if you are using private schools or would use the CofE secondary that wouldn't apply to you.
As Franca says there are many good primary schools in the area.
St Thomas is nice. in an urban sort of way. we liked living there, it's near the centre and the quays and the river, you can walk everywhere easily, it has lots of shops, a good swimming pool. but it is one of the more urban places you can live, and we were already coming from a city so we went for a village instead, but close enough still to walk and cycle in.