To the OP:
Since CO is so much closer, I would agree with some of the others to start your efforts there. This is simply based on what I consider a cost effectiveness strategy. It would be a huge bummer to buy a plane ticket (or gas money to drive) all the way to CA or WA just to find out that mountaineering isn't your thing. You can even learn mountaineering in NM if you like, but I probably wouldn't recommend it to start.
IMO (and I'm not a mountain guide nor do I teach mountaineering courses), you only need glaciers around to learn how to read them. Almost everything else can be mocked-up on snow slopes for the purpose of learning fundamentals. FWIW, I also firmly believe the single most valuable skill in mountaineering is Outdoor Living, as some others have made comments towards. I know this is a broad term, but under this I include: campcraft, backcountry cooking, understanding weather, hygiene, and clothing and sleeping systems for staying comfortable and dry. While not every mountaineering trip is a multi-day event, I still feel it is always relevant to know how to take care of yourself. Sh*t happens to even the best of climbers; it just happens more often and with higher consequences to those who don't actually understand what they are doing.
In terms of being guided, I'd also agree with the comment to go big on Rainier. Might as well, if you can afford it. If you want just some lessons and/or smaller cheaper introductory climbs, a friend of mine operates
Kling Mountain Guides in Durango, CO; so I'll give a shameless endorsement.