Southend is really tacky. The seafront is packed with amusement arcades, down-market caf�s and the type of pubs where you need to watch out for low-flying glasses. The tide goes out for over half a mile, and to get to the water's edge you have to trudge through mud rather than walking over sand.
As Paul points out, there's a direct rail service from Bedford to Brighton, which is packed with good bars and restaurants, great shopping (especially around North Laine) and with tons to see and do.
My recommendation, for a fairly easy drive from Bedford, would be Hunstanton. It's not far past King's Lynn which you can either reach via Peterborough (A1 & A47) or via Cambridge (A428 & A10).
Hunstanton has something for most tastes. There's a small fun fair area (mainly aimed at kids) and a few amusement arcades but there are also good pubs, pleasant caf�s, interesting boat trips, etc. Because Hunstanton faces west, it's protected from many of the cooler winds which plague the east coast (and, of course, you get to watch the sun going down over the sea).
Chris