There’s a very good one north of the City centre (same price range as the Randolph, which when I was there in ’06 was a bit run down), head up the road from St Giles up past St Anne’s college toward Summertown, it’s located right where the road splits I believe. A posh old stately home. Wonderful room for lunch/dinner. Slightly out of town, but one of the two classic hotels in Oxford, along with the Randolph.
EDIT – the Old Parsonage is its name
There’s one right in the centre called “Bath Place” I think, right by the Turf, near New College, it’s very small, pokey and expensive, might be alright, look at Tripadvisor and take a view.