A walk in the countryside can make a great day out with no admission charge to pay or booking to be made. This page lists some suggested walks starting from railway stations featured on this website.
For further ideas I recommend this Pathfinder Guide: Home Counties from London by Train
To find your way I recommend the Ordnance Survey 1:25000 Explorer maps as these are perfect for walking. They show great detail including footpaths, roads, towns and villages.