Just a point, school half term in 2012 is the first week in June. you might want to avoid this unless you have to come then. Exeter is a bit of a way from the sea but have a look at the Devon tourist board site as they have loads of info on the area and also all the places that you could stay have been inspected so you know it won't be grotty. we like the bit of Devon nearest Cornwall - Plymouth has lots to do even though it is a city. Totnes though is a favourite for staying at and then touring around from.
I live in North Devon, but there are loads of lovely places in South Devon that aren't too far from Exeter. Exmouth is a great base ~ plenty for kids to do plus a nice town centre with lots of restaurants. Salcombe is one of my favourites too. There's a beautiful beach plus The Winking Prawn which is fab!
I would also suggest Exmouth, it's only 20-30 mins away from Exeter airport and there's a fairly regular bus service between the two. It's at the start of the Jurassic coast so its long sandy beach has a spectacular backdrop. Sidmouth is also nearby (again doable by bus), which has a lovely selection of more independent shops that you could easily spend the day pottering about in. Exeter itself is also worth a visit - take the scenic 30 min train journey for this. I used to live in these parts, writing this has made me realise how much I miss it!