I would agree with everyone and suggest you stay in Portsmouth, there are a couple of major chain hotels, Holiday Inn and Best Western, where you might get a good deal as well as plenty of B&B's.
Incidentally, and depending on the age of your children, if you have time I would recommend the City museum, it's free and is good for a couple of hours entertainment, esp if it's not great weather. The Spinaker Tower is also really good to take children up. If the weather is clear, you'll have great views.