Hi,
In Surrey there are too numerous places to list (I don't know Berkshire that well). Here's some general favorites of mine.
Newlands corner (first thing in the morning when the viewpoint is in the sun looking over the valleys covered in mist - amazing)
St Martha's, Silent pool and around Albury
Leith hill, Holmbury hill, and Pitch hill. Viewpoints, but lots of beautiful forests and walks. In fact anywhere over the north downs.
Winkworth Aboretum - autumn colour and spring bluebells. Go early and you'll find mist over the lake and boathouse.
Surrey has lots of narrow tree lined roads with high sides and lots of dappled shade in the sun - very unique to Surrey
Ockham common and the pond (Bolder Mere)
Pewley Down and the Chantries (Guildford)
Chiddingfold and Hambledon are very picturesque
Frensham big and little pond ( though not in Surrey, more Hampshire near Farnham)
The hogs back (use as a starting point to explore all the lovely lanes/walks around Puttenham etc)
The River Wey
Lots of National Trust properties too (Claremont landscape gardens etc)
If there's anything more specific you need info on let me know
Hope this helps,
Mark.