Only prob with the Granary is it gets absolutely loused out with golfers. (I dont have a problem with golfers, per se, it just gets busy).
You could try the Boat House at Thorpe Meadows which is about 5 mins drive.
Orton Hall Hotel has a bistro pub attached which is quite nice. Beautiful building.
The Windmill at Cherry Orton is lovely.
Completely agree with Loch Fyne - about 10 mins from the Showground.
Completely agree with The Cuckoo - although beware gets REALLY busy when there is stuff on at the showground.
If you want to sample local food in a beautiful setting you could try
The Falcon at Fotheringhay (Pricy but worth it)
The Red Lion at Warmington
The Chequered Skipper at Ashton
The Kings Head at Apethorpe
If you do any of the latter four, you get to see some of our rolling countryside, beautiful limestone and collyweston stone slate buildings and more than likely a few circling red kites and buzzards.