Haven't got much time, but I live in Eastbourne! My DD's are a bit younger than yours, so I'll ask some friends with older children if they've got any more ideas, but here are a few quick suggestions .......
Bentley Wildfowl and Motor Musuem - Great playpark, cars, wildfowl (obviously), massive picnicing space, miniature railway - well worth the visit!!
Druzillas Zoo (just outside Eastbourne) - Best small Zoo in the country, I belive!! A GREAT day out - bit pricey, but worth it - lots of animals (monkeys, amphibians etc etc), brilliant play areas, big soft play, lots of place to eat, train ride etc etc FAB!
There's a Sealife Centre in Brighton - very good, again, pricey (unless you or your hubby - or someone you know works for the emergency services (police, ambulance etc) cos you can get cut price tickets with a "999 Priority Badge"!!)
Erm, erm, erm .....
Loads of great beaches around - bit stoney though, I'm afraid, check tide times for sand!! Eastbourne and Brighton are both nice, but busy!! For quiet, picturesque type beaches with sand try Cooden nr Bexhill - GORGEOUS!!
Chichester is worth a look.
Lots of theatres (children shows in abundance this time of years, just had The Wiggles in Brighton and Fimbles in Eastbourne!) and soft play (Eastbourne, Halisham, Lewes, Brighton) around.
Eastbourne Miniature Steam Railway is lovely.
Lots of farms, Middle Farm and Blackberry Farm nr Eastbourne, we've got Severn Sisters Sheep Farm is worth a look as is the Ashdown Forest Llama Farm and Ashdown Forest is where Winnie the Pooh was invented is fab (you can go to "Pooh Bridge" and play "Pooh Sticks"!!).
That's just off the top of my head!! You have choosen a great place for a holiday!!
I'll be back again when I've thought of more ........