The classic Ilmington route. I tend to walk it one way but run it the other. It depends if you want the hill at the beginning or half way round.
I think the views are probably better if you go the Foxcote Hill first direction. Compton Scorpion Hill is shorter then Foxcote Hill but is a challenge none the less (still not managed it on a bicycle)
Great views at Redlands Barn. At Compton Scorpion Farm there is a large field of ridge and furrow, all man made in medieval times and rapidly disappearing as farmers flatten their fields out.
Look out for buzzards, red kites, deer and muntjac with the occasional owl at sunset.