I was down in Eastbourne last weekend with a friend of mine, as opposed to going to Brighton.
There are a number of relatively cheap bed and breakfasts (and hotels), many of which have a sea view. I didn't do much there, besides go on the beach and sample the local version of fish and chips, but it was great to get away from the rat race.
If you ever have the chance to spend more than one night there, do it!