Thanks Andy, you've said everything that I was going to say, since Dover is my home town! However - you do need a car for St Margaret's as it's a bit of a way out of town, but it is pretty.
Granny, Dover town is not up to much (it's small and quite run down so not a lot of shops, but we do have a de Bradelei factory outlet!) but it's got a good Best Western Hotel on the seafront, and behind it is Cullins Yard bar and restaurant which is very good. It's right on the harbour front, if you can get a sea view.
Depending if you are driving or on public transport, Dover has good rail links to Deal (which is lovely) and Sandwich (ditto) and the train also goes round the coast up to Ramsgate and Margate. Canterbury is a direct train line half an hour away. Folkestone (bigger town) and Ashford are on the other train line. Folkestone's got the Grand Burstin Hotel which is right on the harbour front. You can get a 45-minute bus ride down to Hythe which is well worth a visit - the Royal Military Canal, the Romney Hythe & Dymchurch miniature railway takes you down to near Dungeness, and the shops in Hythe are quaint.
Although Dover's not a shopping hub, it has some fabulous history - you can spend all day in the castle and the underground tunnels, it's a great place, then there is the Bronze Age boat in the town museum, the Roman Painted House, the fortifications up on the Western Heights, Langdon Cliffs where you park and can spend lovely hours watching the seat traffic up and down the English Channel - and you can see France on a good day. You can always take a ferry crossing too - lovely on a calm day. Bring your passport!