I depends on how you're going to get from home to Ascot, but if you'll be coming in on the A329 there's a couple of options.
Slightly out of your way, albeit still quite close, is
Windsor Great Park which has lots of nice places to wander around and some good scenery. And closer to Ascot is
Virginia Waters which has a rather nice waterfall and makes for a pleasant stroll.
Follow the A320 out of Ascot towards Bracknell and you'll eventually get to a Mercedes garage on your right called Greenoaks. Just after that you'll come to a small-ish roundabout, and if you take a right into Long Hill Road you'll see signs that direct you towards
Lily Hill Park which, to my mind, is Bracknell's biggest secret. It's a lovely place to have a wander around and is in the most immaculate condition.
Bracknell's not really got much to offer in itself, but it does have
the Look Out and its surrounding areas, which make for a nice walk and feature some nice scenery. It can get quite crowded and it's hardly what you'd call wide-open space though.
Then there's always
Pope's Meadow in Binfield,
Dinton Pastures which is somewhere between Winnersh and Hurst and a few others whose names escape me for the moment.