One of my favourite spots in the local area. Wellingtonia Avenue consists of around 100 Californian Redwood trees and was planted in 1863 to commemorate the Duke of Wellington.
Around 20 years ago a fungus threatened to wipe out the trees, and one died, but fortunately the rest were saved.
Even if you just drive down the road, it is well worth visiting, however at one end there is the Finchampstead Ridges which are worth stopping off, and a short walk back down the avenue from there is Simon's Wood and Heath Lake.
If you can't drive there, the Avenue is around two minutes walk from Crowthorne Railway Station (one stop down the line from Wokingham).
Berkshire is a very busy region, what with there being a great deal of industry and London being commutable distance. If you do want to get away there are some really nice parts of countryside. Twyford Lakes is a wildlife reserve where you can access easily by train or car and do a 6/7 mile walk round the water through the woods - I cant guarantee you wont bump into anyone - in fact when we went we were surrounded by a group of noisy people doing orienteering but when they arent around it is very peaceful - look out for a country pub half way round so you can have a refreshing drink before you continue on your journey!