Hengisbury Head near Christchurch.
You can follow the paths that lead over and around the nature reserve which is also important archaeological site. In the Bronze Age Hengisbury Head was a cemetery, with barrow burials. Then later Iron age people settled and exploited the ironstone found in abundance there. There is an excellent visitor center where you can explore the history and natural history of the area.
All in all, for the price of a car park ticket (which you can avoid if you don't mind parking a little way further along the entry road), this is a pretty special place to visit.
Good buggy and wheelchair access over much of the site. Toilets, including changing facilities at the visitors center. Cafe. Ample pay and display car parking. Good cycle routes around the area if you're coming by bike.