The Rock Restaurant
16 Landseer Road, Westbourne, Bournemouth, BH4 9ERH. Tel: 01202 765 696.
Although this might be above Tesco, but it is in a former church and when you walk up the stairs you will enter a really nice setting with vaulted arches and stained glass windows.
They do a good lunchtime deal and I've always enjoyed my food there.
Website: Rock Restaurants