I don't live in Southampton but close by.
Whilst I don't pretend to be an expert on the hotels there, here are a few:
4 *The Southampton De Vere (V. NICE) Rooms I expect approx £150 per room per night)
3 star Hotels would be Novotel or Ibis which are next door to each other approx £55 to £60 per night.
Nothing spectacular about these as they are a chain of hotels but clean and not a bad price.
Try a search for them
You can easily get to the port from here.
If you are staying a few nights there is a Marina called Ocean Village up the road with restaurants and a Cinema.
Plus if you want shopping get a taxi to West Quay shopping centre, again only a short ride away.
Hope this helps.
I'm going on the Celebrity Summit from Fort Lauderdale in October so doing the same seach in reverse but think I'm nearly there.