Lived in Salt Lake for 21 years, until 2002, and my kids both are still there, so I visit often. Top nursery in my opinion is Cactus & Tropicals up on 20th East near 2700 South. They have a fabulous selection of exotics as well as some unusual outdoor plants for sale. Their website is excellent, too.
The other one I use for basics, supplies and perennials when I'm helping my daughter with her garden is Millcreek Gardens down on 900 E between 3300 and 3900 South.
I must admit I've never checked out their begonia selection at either place. The dry air and alkaline soil isn't particularly friendly for begonias and such, is it? Keep it in the bathroom or kitchen, somewhere with a little humidity and you might do fine, though.
Thanks for the nursery suggestions. I live in Northeastern Nevada where the environment is fairly hostile for growing much of anything, but I have a small collection of about 40 begonias which are happy as houseplants with humidity trays. There were number of different begonias in the outdoor plantings at Red Butte Gardens in Salt Lake City. They seemed to be thriving.
Will have to go to Red Butte next time I visit, thanks! They do have a stream flowing through the gardens there, I recall. It likely helps with a little increased humidity to make it work for begonias. Btw, they have a plant sale in the springtime where you might be able to get some starts of their begonias. Check their website.
Nice way to keep your home healthy and humidified in the desert, with a begonia collection! I've just started with begonias in my shady border area here. So far so good, but we've had a couple of tough winters (for Florida) so we'll see!