Hastings Underwater World (it's no longer called the SeaLife Centre) isn't bad. It mostly has native fish and invertebrates. The main features are an underwater tunnel (dogfish, rays, things like that) and a shallow pool for rays. There are questions on the wall with buttons you press for the answers which the kids'll probably like. It's also right where the fishing fleet is, so you can see the net huts and the fishing boats on the beach. It's main problem is it's small so it wouldn't be a whole day out. It can also be pretty crowded due to the size.
If you're prepared to do a little bit of walking, you can walk along to the West Hill lift and go up to the Smugglers Adventure. It's a set of caves with a smuggling musuem (lifesized talking models and the like). You should get money off the tickets if you have Underwater World tickets. The two go together well for sea-loving kids. I wouldn't recommend it for very small ones though due to the walking, both walking along to the lift and getting around the caves.