Haven't been to natsunoya in a long time. I think it is the last of the old Honolulu tea houses. I understand they are making a serious effort to refurbish it, bring back the quality it used to have.
Waioli is not a tea house, it does western style teas, lunch/brunch type food. Think English Tea room, not Japanese Tea House. (the food is good, service is 'relaxed')