Unfortunately there's zero chance of returning to the Rio Grande or UP stations. The tracks through the downtown area are long gone.
We were just in Salt Lake last week, stayed at a Homewood Suites right next to the old Rio Grande station. It's owned by the Utah Historical Society, and is very well maintained, but landlocked by roads on all sides. At the time we were there it was holding an exhibit on Rio Grande passenger trains, but we weren't there long enough to tour it. Our room had a nice view into the windows of the main waiting room, which was nice.
The old UP station is merged into the Gateway Shopping Center, and has some stores in it along with a grand hall (the old passenger waiting room). The entire track area is filled by shops and fountains. This kind of snuck up on me, I didn't realize until I was in the main plaza area that this was the old depot. You can see a shadow on the west side of the roof where the UP shield used to be mounted to the copper roof. Seeing so many old depots destroyed, it is nice to know this has been kept in productive use, but it'd be nicer to see as a station. I didn't get inside, but there used to be some nice murals in the waiting room which depicted historic scenes from Utah railroad history. UP spent a fair amount of money to restore the waiting room ceiling in the 1970's if I recall right, in time for the bicentennial. At one point the south part of the station was filled with train simulator equipment for engineer training.