>Salt Lake City well within 3 hours of any resort in Northern Utah. There are 7 within 45 minutes of the airport. What resorts are you thinking about? You should be able to do plenty of hiking that time of year.
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rci.com lists 21 resorts in UT with two bedroom units. They are in towns with names like Park City, Henefer, Brian Head, St. George, Garden City, Eden, Snowbird, and one ("The Kimball") right in Salt Lake City. It may be that none are available right now. We are about to call and see what we can get. The higher mountains are of more interest to me because that's what I haven't seen on previous trips. But it may be better to seek lower elevations, and there are many such areas I have not seen at all, some with RCI resorts in the region.

I'll let you know what turns out to be available.