Well Historic Quay is like an old reinactment of maritime life in Hartlepool, Well worth a look. we have one of the oldest battleships there too called the HMS trimcomolee (bad spelling). Lots of things to see and do in there too. They have recreations of the old shops movies to watch and a guided tour of our "fighting ships" which tells a story.
Other things to do really depends on what you enjoy, there is a retail park just behind the ground and our town centre is about a 5 minute walk. best advice is just turn up and have a look around
EDIT: We also have the Hartlepool museum situated behind the Historic Quay also worth a look if that is your sort of thing. You can interact with many things there and can make an interesting area. Cant really think of much more off the top of my head! safe journey