Best area for Alpine inexperience?

Hi All,

Two Australians travelling around North America. Been in Squamish 2 1/2 weeks and looking to move on. Planning head east, do a bit of sport climbing at lake Louise before heading south to Wyoming ( Tensleep, Devil's Tower) and Idaho (city of rocks).

I would really like to climb a mountain, something that doesn't require any ice experience and more friendly to someone with no alpine experience. We have plenty of rock climbing experience, climbing up to 10c in Squamish.

Would there be any alpine areas you suggest that are not going to leave me frozen and dead?

Areas that I have noticed are in the general area of our travels:

Bugaboos
Wind river range/grand Tetons
High Sierra

Cheers

Jason