Another vote for Portsmouth Harbour. I think the naval dockyard (right by the station) is one of the best days out going with kids. You can also go up the Spinnaker Tower and there are lots of great places to eat - all a stones throw from the station.
Freind of mine at work wants a day out at the coast tomorrow to give his boys a day in the fresh air and wants somewhere with good train links from London where the train station is near the seafront (therefore Brighton has been dismissed). Any ideas for Essex, kent coast etc?