In Brighton

Brighton Seafront and Pier - www.brightonpier.co.uk
The Royal Pavilion  - www.royalpavilion.org.uk - magnificent royal pleasure palace built for George, Prince Regent, at the turn of the 19th century.
Volks Electric Railway - www.volkselectricrailway.co.uk - claiming to be the world's oldest operating electric railway, it runs between Brighton Marina and the pier.

Historic Houses, Castles and Gardens
Nymans - The National Trust - www.nationaltrust.org.uk - 20th-century garden, set around a romantic house and ruins, in beautiful woodland
Borde Hill - www.bordehill.co.uk - garden, parkland and woodland 
Wakehurst Place - www.kew.org/visit-wakehurst - Country estate with ornamental gardens, woodlands and Elizabethan mansion.
Lewes Castle - www.sussexpast.co.uk - Castle of Norman origin with an impressive 14th-century outer barbican gate.

Things to do with the kids
Sealife Centre - www.sealifeeurope.com - The oldest operating aquarium in the world housed in wonderful Victorian buildings on Brighton Seafront.
Lavender Line Steam Railway - www.lavender-line.co.uk
Bluebell Railway - www.bluebell-railway.co.uk - The volunteer-run Bluebell Railway operates restored steam trains throughout the year on their 9-mile line, running through the Sussex Weald.
Ten Pin Bowling - www.bowlplex.co.uk
Drusillas  - www.drusillas.co.uk  - Zoo and Family Fun Park

Activities
Sailing & power boating tuition  - www.greenactivebreaks.co.uk - also based at Brighton Marina.
Power Boat & RIB Charter - www.fullthrottleboatcharters.com
Watersports - www.thebrightonwatersports.co.uk - including boat charter, wake boarding and waterskiing. 
Scuba Diving - www.academyofscubadiving.co.uk & www.newhaven-scuba.co.uk
Walking on The South Downs - it's not just about the sea...

There are a lot more ideas on the following sites:

www.brightonmarina.co.uk  
www.childfriendlybrighton.co.uk 

www.brightonvisitor.com  
www.visitbrighton.com  
www.ukbeachdays.co.uk