There is a Novotel and an Ibis at West Quay right opposite the dock gates. They are very basic hotels, if you want better quality there is the Devere Grand in the same are.
We have booked Jurys Inn nearby- I hope- they say its only 10 mins away by taxi- £69 a nigh.
We have stayed at the Southampton Park Hotel before and found it to be excellent...only a 5 minute taxi ride away from the docks.
Try Premier inn eastleigh its just off the motorway and reasonably price i always stop there when i go to southampton.