A couple of quick recommendations:
Since the Zephyr gets in here around 10:30-Midnight, you'll want a hotel. I agree with trying to find a hotel that will pick you up from the train station. Or get a couple of cab company numbers ahead of time. Yellow Cab 801-521-2100 has their dispatch about a block or two south of the intermodal hub. Ute Cab and City Cab are also close. But there seldom seems to be cabs waiting at the station. Uber and Lyft are both in Salt Lake as well.
The station is on the western edge of downtown but there's not much nearby at that time of night and there are a couple of problem blocks/corners nearby so I recommend getting transportation out of there. If the Zephyr is relatively early you might be able to catch some of the last Trax trains into the heart of downtown.
It's a cute little downtown. I'm blanking on what to do (I live here and take it all for granted)... The obvious answer is to check out Temple Square - it's beautifully maintained gardens and fountains and various little building around the Salt Lake Temple. The staff is friendly but shouldn't try to push Mormonism on you and it's really a lovely couple of blocks. There's a tall white building by the temple called the Church Office Building and I believe they still have an observation deck up on top. It's only 26 stories but you can get good views of not only the Great Salt Lake but of the mountains and Avenues on the north and east side of the city and maybe you can spot other things you'd like to see like memory grove (a park at the base of City Creek Canyon that's quite pretty) or the Cathedral of the Magdalene or the new-ish fancy library or the old city-county building.
If you're a rail fan and are feeling adventurous, you can take the Front Runner train up to Ogden. There's a small rail museum at the old train station up there with a nice variety of engines. It's about an hour up and an hour back and you'll want to make sure you catch the Park City Connection in the evening, but the last PC Connection leaves at 6:11. Since the Zephyr gets in here at night, the Front Runner is a good way to see the scenery by rail. Ogden has some nice little diners and bars near its Union Station. As long as you leave by around 4:00 pm you should be fine getting the connection... But you'll also be seeing some nice mountain scenery on the connector bus and around Park City.
And, of course, you'll get plenty of awesome mountain scenery on the Zephyr.
