Campgrounds in & near major cities have the deck stacked against them, to some degree. The location is likely to be inconvenient, because campgrounds need lots of land, which is expensive within the cities. A campground is not as profitable per square foot as other land uses, such as shopping malls or offices, but they still have to pay property taxes. And it's a seasonal business, to boot. Since people won't pay as much for a campsite as they will for a hotel room, campsites within the city limits must be smaller to maximize revenue. Where city campgrounds can shine is with services (selling passes to local attractions, staff who can answer questions, campground store) and campground amenities (clean shower/toilet blocks, pancake breakfasts, horseshoe pits, etc.). Campgrounds outside the city limits can offer more reasonable rates or larger sites, but they're not as conveniently located; it can be a 25-minute drive just to get to a grocery store or gas station.

Campgrounds within Calgary

Due to the constraints mentioned above, there are only two campgrounds within the Calgary city limits. 

Calgary West Campground: The only campground within the city limits, Calgary West is just north of the Trans-Canada and a short distance west of Winsport's Canada Olympic Park. The sites are stacked up along a hillside. It's about a mile (1.3 km) to the nearest Calgary Transit bus stop.

Symon's Valley RV Campground: Newly reopened in 2014, after being closed for several years for redevelopement of the site, Symon's Valley is located next to a new farmer's market in NE Calgary. 

Campgrounds near Calgary

Calaway Park RV campground: Located on the Trans-Canada Hwy (Hwy 1) about 20 minutes west of the Calgary city limits, and right next to the Calaway Park amusement (fun) park. The sites are very open, with lots of tall poplar trees that may provide shade but do nothing to screen you from your neighbours. They have an unserviced overflow area which is used for camping on busy long weekends; that overflow area is basically just a large grassy space.

Mountain View Camping is about 3 km east of the city limits, on the Trans-Canada Hwy (Hwy 1) between Calgary and the town of Chestermere.

Whispering Spruce is north of Calgary on the QE2 (Hwy 2). It's in Balzac, not far from the huge CrossIron Mills mall, which it predates.

Aspen Crossing is about 25 minutes southeast of Calgary

Finally, there are two campgrounds in Cochrane, Alberta, which is about 25 minutes west of Calgary on the Hwy 1A: Bow Rivers Edge Campground and Spring Hill RV Park

Washing RVs

There is an RV wash at the car wash in NW Calgary just NE of the intersection of the Trans-Canada Hwy (Hwy 1) and Bowfort Road. It's tucked in behind the COP McDonald's and the Four Points by Sheraton Calgary West. Look for it on Google Maps; it's the entire L-shaped building:

There are other places too, but this one is conveniently located on the Trans-Canada on the western edge of the city. They've recently converted some of the bays from wand wash to automatic wash.