Since Byzantine is what you are comfortable with, I assume you know St. George GOC here in Albuquerque? As far as I know, other than St. Pishoy COC, they're the only game in town for Orthodoxy. Nice folks. Met one of their parishioners in line at Costco a few months back, of all places, and all my friends from church tell me that their church is beautiful and their food/cultural festival is a lot of fun. Never been to either myself, though I might have to go one of these days, if I get the chance.
Where do Eastern Catholics go, by the way? The only place I know of is Our Lady of Perpetual Help on Alvarado (?), which I've also never been to (neat website, though). I'm just curious because we have two Eastern Catholics who regularly come to our liturgies and say that they like it better (one of them said "it's really Eastern, even though it's in English", but I have no idea what that means), so I get the impression that Eastern Catholicism in this area leaves something to be desired.
I bet you almost anything that the guy you ran into was one of my closest friends - he's going to seminary next fall. Love that guy. We both love Costco, too. :-p He's right - St. George's is the most beautiful church in the state.
There are Greek, Russian, and Antiochian (convert, not ethnic) churches in Santa Fe, and there's All Saints of North America (OCA) off of 4th Street by El Pinto (Fr. Nikoley) in Albuquerque as well. Fr. Joshua has his hermitage down in Belen - also, there is a monastery up by Abiquiu - Antiochian or Russian? I can't remember.
Most Eastern Catholics go to Our Lady of Perpetual Help. We have a large extended family of Chaldeans coming here, some Melkites/Antiochians, and some Syriac Christians. Honestly, they're so jumbled up, I honestly don't know who's Catholic and who's not - none of them really care. They view it as all the same. We also have Ukrainian Byzantine Catholics coming here too, and some Maronites.
We had a Maronite mission here but that fizzled after one Maronite family moved to Florida.
There is an Indian mission of some kind (don't know if Malabar or Malankaran) at Our Lady of the Annunciation. There are also various Eastern Catholics scattered all around the city at various Roman parishes.
As far as St. Pishoy goes, I've met George from there - he visited OLPH a couple of times and was friends with a Maronite friend of mine who's since left.
There are also at least two really tiny really crazy tiny Old Calendarist is True Greek Orthodox Catholic Church of America or something like that here . . . they came to Orthodox Christian Fellowship at UNM (I go occasionally) and were trying to convert people.
OLPH is pretty Eastern, though, I would say. Love that place.