There is a recently built swimming center called the Mountbatten Center with a very affordable 50m swimming pool and track and there are plenty of parks around the city. I used to take my kids on continuous walks on country walks – Southern Hampshire is a great place for these walks and if you want to go further, you don’t need to be far west from New Forest or Downs to the east. The Hilsea streams are located on the northern coast of the island and are great for kids to explore – in the south you can take the Seaplane to the Isle of Wight, walk around Henry VIII’s castle or take a tour fair.
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The sea surrounded Portsea Island, great place for children 12 miles from Portsmouth is the old Butser iron farm site which has all kinds of buildings reconstructed from the Neolithic to early Saxon and is open throughout the summer. The schools are very different but Admiral Lord Nelson School is great for both my child and many others. Both of my children were taken to local colleges before they finished and the University of Portsmouth gave a series of public physics lectures that local schools were invited to participate in.