Welcome to the sport!
There are many places for you to go. If you want a good combo of trail riding and MX then Jordan River Raceway has a little of both. JR has bathrooms and a nice grass area with trees. The track out at tooel has a kiddie track as well as more advanced courses. It also has a nice grass area with a couple of picnic tables. These are the most 'civilized' in terms of facilities and within a reasonable distance from SLC.
The track out at Price has some really fun trails/riding areas nearby and except for the downhill jump(major pucker jump) it is a really friendly track to roll or go fast on . Probably the best overall family experience for a wide, open area is 5 mile pass but no mx tracks (plenty of jumps however).
There are a lot more options but they tend to be many hours away.
-mx