Hungry Monk in Jevington is nice. May have to book in advance. Or the Eight balls, also in Jevington (although it's a pub does nice food).
Couple of other good pubs are The Old Oak, Arlington and The Yew Tree (which will 95% certain be fully booked)
When I was doing some elecrtrical work in the Wish Tower Nora Batty was in there, so it can't be that bad.
Chatsworth is nice (although I've never eaten there)
Got it from ..... http://www.visiteastbourne.co.uk/specialoffers/default.htm
"Special Three Course Mothering Sunday Lunches available at:
The Albany (Lions) Hotel £15.50 with a free gift for mum
The Chatsworth Hotel £18.50 with a free gift for mum
The Mansion (Lions) Hotel £14.50 with a free gift for mum
The Cumberland Hotel for £13.95 and
The Wish Tower Hotel for...