One other note about public transportation, your game ticket allows you free passage on game day. Definitely recommended instead of trying to find parking.
Other Attractions – I would say Temple Square would be a must see for any out of state visitor. Park City would be another place I would recommend visiting, plenty to do in both the summer and winter.
RedLine listed a lot of the good food options. A second from me on Red Iguana. Hires Big H is another place I would recommend on the simpler side. Sort of a standard diner type place. Stadium food is pretty standard, nothing spectacular. Then again, I’m a basic dog and a Coke guy so I’m okay with that.
Safety – as long as you’re not a BYU fan you should be okay. There is no where around the stadium that I would consider unsafe and I would say our fans are generally hospitable to neutral from what I’ve seen and heard from visiting fans.