If it helps, portsmouth fc have a pre season friendly away today (my lot are going), so they can't blame football hooligans there.
I would think down by the sea would be ok, especially further away from Southsea pier. If you head east from there, there is a quiet section of beach with a lovely coffee shop (coffee cup). As it is a bit of a walk from the centre, and has nothing to destroy, I would expect them to avoid it. There is parking nearby as well.