We have two organizations in our area - one is an Alano Club and the other is a Fellowship Club that have their own private locations serving as meeting & gathering places for AA members and host multiple AA & Al-anon meetings each week. I would expect a large city such as Denver would also have something along those lines.
Ditto some of the other posters - several of the hospitals & recovery center in our area offer meetings. The churches are often used because they have inexpensive rent.
Religion is not a focus in any of the meetings I have attended. HP is in some readings, and individuals may reference their personal beliefs when they share. They often say the Lord's Prayer at the conclusion of the meeting, but you could respectfully decline to participate, or join the circle and not recite the prayer; I do not believe any one would take issue with that choice.