That was at my birthday 3 or 4 years ago, we went to the Tea House on Los Rios in SJC. They do a really nice tea for not too much money (compared to what some places charge!) And they're very friendly to the whole "dressing up" thing.
The hat, incidentally, is just a few yards of tulle wrapped around a cheap straw hat from Michael's and pinned on

Amazingly works quite well.