In addition to The Oasis, the cute Santa Fean highly recommended Longevity Cafe. I have to say, it's very nearly the best cup of tea I've ever experienced. I may even beat out my all-time-favorite, Fritz (in San Francisco), but I'll have to think about it more.
Longevity Cafe is a place that just gets it. They've got a huge tea selection, a fantastic menu of herbal infusions, a strong menu of asian foods, and friendly and helpful staff behind the counter. They've got the right music (trancy, mellow world beats), the right lighting, comfortable chairs, plenty of couch space, happy plants, gurgling fountains, beautiful artwork with a consistent theme... I'm not a metaphysical guy by any stretch of the imagination, but this place just radiates positive energy from all corners. It's obvious that a lot of love and hard work went into making this understandbly the first place for a cup of tea Santa Feans recommend.
Oh, and to top it all off, they have 802.11 access and lend out wireless-enabled laptops for free. How cool is that.