Another vote for Gunwharf Quays,shops, cinema, places to eat- can't go wrong. I personally think the parking is a tad pricey though and parking spaces a bit too tight for my liking.
The Polo courtesy car is £12 for the day and you need to fill it back up, whatever you use. It's actually quite a nice little car to drive. Better ask Kate if it'll be available first, if you plan to use it.
I think the aquarium is down in Southsea by Clarence pier amusement park. It's not very far from Gunwharf at all, maybe a 5 min drive.