I live in Calgary and drive past a KOA campground every day on the west end of the city on the transcanada hwy. Another option is the Symon's Valley Ranch Campground which is on the north end of the city. Both are RV friendly, provide good access into the city, and can be googled online for more info. If you're interested in mountains + golf, the Mount Kidd RV Park is a good option about 1.5 hrs west of Calgary in Kananaskis Provincial Park. You can book online, which I would advise since it seems to be pretty popular. Never stayed there myself, tho.
If you're up for something quieter and more scenic, our favourite spot is the Tunnel Mountain Campground in Banff National Park, about 1.5 hrs west of the city. They have full hookups or electrical only and are very RV friendly. The rates are reasonable by local standards (can't remember what we pay) and the spots are very quiet. You'll have to pay a single entry fee at the park gates of around $10, but they also have weekly rates - well worth the expense if you ask me. Again, you can book online.
In terms of navigating the city, bear in mind that Calgary is a booming city of 1.1 million people (most transplanted from TO and your neck of the woods! ;-)) and the majority of people drive vs. taking our (crappy) public transport. Rush hours are pretty brutal and there is a construction everywhere. If I were towing, I'd definitely want to avoid the hrs between 6-9am, 11:30-1pm, and 4-6pm weekdays, especially if I were coming from the south on Glenmore, Macleod or Sarcee Trails - east or west it's not too bad. Traffic is usually slightly less on fridays as people leave early to their weekend homes in Invermere or Canmore, and slightly worse on Mondays as they come back. Weekends, the roads are always busy between 11 - 5pm.
If you stay past June into the first week or so of July, you'll be getting into the Calgary Stampede season. At that time I imagine that ALL the local camp grounds book solid as an addition few hundred thousand people flock to our fine city. It's worth taking in, if you happen to be around, btw. Not too many places left on earth you can watch nightly rodeo and chuck wagon races!!! Talk about your thoroughbred towing vehicles!