grab a city weekly and a SLUG from almost anywhere and check out the events sections in there for things to do. summer here is really full of that kind of stuff, it is starting to wind down now but come winter there is tons of shit to do at the resorts.
there are a lot of free/inexpensive concerts and things like that, especially if you are over 21. if not, it seems there is always a lot of stuff going on at the U now that school has started that is generally not 21+ including ski movie premiers and the such.
for a few more saturdays there is a big farmers market in pioneer park, but it is kind of a shit show. also, the library has events all the time and there are festivals downtown fairly often.
really the best and cheapest thing to do near slc is play around in the mountains. if you are into climbing, there is an incredible amount of all types in the cottonwoods alone. there are also tons of hiking trails where you can do seriously hairy lines with exposure or mellow paths to incredible views. there are also good mountain bike trails from what i hear (i don't do it myself so don't hold me accountable if they aren't that good).
the wasatch is nearly as fun in the summer as it is in the winter.
