Did you know that Hampshire is the oldest shire county in England? There is evidence of settlement from 12,000 BCE and Winchester was later settled by the Romans, who named it Venta Belgarum and made it their administrative capital. The Saxons settled in what is now Southampton, calling it Hamtun. The surrounding land, or scir, was called Hamtunscir, which is recorded in the Domesday book as Hantescire. You can see National Trust sites in Hampshire here or Hampshire County Council have posted some ideas for things to do for the day here
Link to a really excellent Wikipedia article on the history of Hampshire: https://en.wikipedia.org/wiki/History_of_Hampshire
