How about the Perch Inn, down Botley Road by Port Meadow? It has a lovely beer garden, but has recently changed hands so I can't comment on the food.
The car park is of medium size, maybe half the size of the Trout's. It's usually more than half full at the weekend, as people park up to walk the dog etc. For a few cars I suspect it shouldn't be a problem.
There are a few nice pubs up in Cumnor too, but I can't think of the names at the moment. If needs be I'll drive up and do a rekky
