Having grown up in the area - I'd agree with the above as a good start.
- Tangmere has the world record setting Hawker Hunter and a replica of the Spitfire prototype. Worth a look.
- Eastbourne Redoubt and Newhaven Fort are both full of history.
For the older history, Pevensey castle is interesting, as is Bodiam castle. The Battle of Hastings re-enactment is around about now over in Battle (with Battle Abbey).
A27 across to Portsmouth is do-able, though it feels like a long drive when you're doing it. There you have the D-Day museum and the historic dockyards, Mary Rose and Victory.
Further afield in the opposite direction is Dover castle. If you get there make sure you book onto the underground hospital tour early as there's only a limited number of spaces. The upper bunker was central to D-Day.