Greys Court looks good.
Blenheim Palace itself is closed on Tuesday. I think I went there decades ago, but worth going again at some other time.
You can almost certainly cycle through the grounds though. They have daft rules about you supposedly not doing, but sod that - had breakfast there on the bike last year and fired up the espresso pot by the lake. Wonderful. Can send you info on a good gate to get through if you want. Then you can cycle out through the main gate giving them a cheery wave.
Pedestrian access is free though they like to obscure this fact.
As above, windsor great park is wonderful for cycling through. It's massive. No daft rules about bikes but cars are not allowed in most of it.
Can also recommend in that neck of the woods the air force memorial - wonderful spot, rather moving - used to be a regular stop on rides i used to lead london to windsor. All appreciated it i think apart from a posy german, stress on posy.
https://www.cwgc.org/find/find-cemeteries-and-memorials/109600/runnymede-memorial
You can by the way walk up on to the top to see the rather more peaceful planes taking off in the distance from Heathrow. Lots of individual memorials around the base, many recently tended with flowers, letters etc from relatives. Not just Brits, folk from all over.