Oh - I just wrote you a massive post and mumsnet ate it! Grr. Anyway, here it is again:
The shopping is quite good in Winchester, although most of the shops are fairly expensive! There are lots of nice shops in The Square (by the cathedral) - including the Hambledon, which is one of my favourites for lovely homewares and clothing. Parchment Street is worth a look for its little boutiques, and the High Street has all the usual suspects including Jigsaw, Cath Kidston, Joules, Hobbs and that sort of thing. There's a great secondhand bookshop on George Street and a few nice antique shops scattered around.
The restaurants are nothing special, really - lots of chain pizza/pasta places. Pizza Express is a good place to lunch, though - it's in a lovely old building overlooking the mill, so you get a great view of the weir. If you're after something more expensive you could try Hotel du Vin or Brasserie Blanc, and if you stroll along Jewry Street (at the top of the High Street) you'll come across lots of restaurants and bars including a Dim T and an American-style diner.
Winchester's so old that there are loads of touristy things that you could go and look at, but I think the only unmissable one is the cathedral, which is very beautiful. The crypts should be open by April, so you could pop down there for a look at the Gormley sculpture. While you're there, it's worth taking a look round the Cathedral Close and round by Winchester College as well.
Hope this helps!