You have to go see a Jazz game at the Energy Solutions Arena, it is so fun to be there in person! The higher the seats, the steeper it feels so use caution if taking a younger child. They have really good icecream there during breaks, and even the highest seats have a good view!
I took my daughter to see the princess on ice when she was 5. I don't think you can get a bad seat at the Energy Solutions Arena and it's always loud (sometimes good/sometimes bad= take ear plugs just in case). We had fun going, there were lots of vendors after the show. I felt like it was a clean and safe place. I would suggest planning ahead for parking though.
Energy Solutions Arena (formerly the Delta Center) is a great place for events. It is located right downtown Salt Lake City and very accessible to get to. I have been to everything from a Neil Diamond Concert, to comedians, to Utah Jazz games, to little kid's shows at this arena. This place has it all for everyone. The prices vary with each show, but are competitively priced. It is usually clean and well taken care of.