Southampton is not the most exciting place in the world. There is a big shopping centre if that's your thing, or you could head up to the common if the weather is nice. It's a big park with ponds etc, very pretty. Watch out for flashers though!! I'd probably find a nice coffee shop and watch the world go by. The docks are a little bit interesting, but very commercial. If you like looking at big boats then Ocean Village is quite good.
I pass through Souyhampton frequently, and yolande makes it sound worth a stop. I don't think I want to watch out for flashers though, because I don't like them.
If you've got a car you could visit the New Forest - only half an hour drive from Southampton and loads of places to walk, nice pubs for lunch etc. Or if you haven't you could take a walk around the city walls and look at the old part of the city, then wander down to Ocean Village where there are now a couple of nice bars overlooking the marina.