Southsea is actually quite nice, it depends what you're looking for…
I lived in Southsea when I was a single gal. Lovely flat on the seafront, free live music every weekend, farmers markets every month down Palmerston Road, walking distance to some alright bars and Gunwharf Quays. But Southsea and Old Portsmouth are the only nice bits really.
Towns just outside of Portsmouth are Chav magnets, Chichester is nice, quite posh and very expensive.
I live in the New Forest now, settled with my other half and am very happy, lots of forest, beach and a nice villagey atmosphere. Only a stones throw from Southampton town too if we miss the city.