Yeah, the great thing about Utah is that we have great and affordable public golf courses. Every time I play at award winning golf courses in other states, paying $100-150 per round, it frequently reminds me that I can play an equivalent or nicer course in UT for $10-30 per round.
I agree on the PC Municipal course. In late August, call a week earlier and get an early tee time (approx 7:30am). This is a busy course, but the early morning tee times are nice and the temps are wonderful as the sun comes up over the mountains. We do this every year and it is typically about 55-60F when we tee off #1, and then we enjoy most of the round at about 65-75F.
I also agree about the Mountain and Lake course in Midway, but I think that Soldier Hollow is nice enough as well. Not as nice as several others though. The Gold course is very difficult and LONG. The Silver course is much more manageable. If I had to choose though, I would certainly choose the Lake course first, then the Mountain course.
If I were in your shoes and had a 4 day weekend in PC. I would golf PC Municipal and if I could get on at either Promontory course I would do that. I know the Dye course allows 8 public tee times a day, but not sure about the Nicklaus course. So call those two well ahead of time to see if you can get a time. Then if you wanted more golf, I would take a very nice drive to Wasatch Mountain State Park courses. I wouldn't take the freeway (I-40) to get to them, but instead would opt for the more scenic drive up over the mountain on Highway 224. Since you are staying at Deer Valley, the 224 goes right through there, just hop on it and start driving south. It is a very beautiful drive, even in August when everything else is starting to dry out.