Okay, time to write a better reply!
The two main sites I use for rentals are www.rentfaster.ca and www.kijiji.ca. I don't use Craigslist, as it's full of scammers. You can look, just be careful - be careful with ALL sites as even sites like Rent Faster have scammers using them.
The good news is I found some decent looking properties within $1200 with three bedrooms. I can't say they're 'good quality' because I'm just looking at pictures, but the areas in the city are good. These are on Rent Faster. I'll list the IDs.
Listing ID: 36851 - Location in Abbeydale which is a nice neighborhood for the most part. Location near the edge of the city. The 45 bus can take you to the C-Train at Marlborough Station for easy access downtown. There's a hospital near Marlborough station too, along with a lot of professional offices (jobs!) and shops.
Listing ID: 21358 - Located in Rundle - my sister-in-law lives here and it's a nice area in the NE Calgary. It's a little more central than Abbeydale. This building is run like a complex, so they will probably require a year lease. The kitchen is small... like really small... and one bedroom is tiny too. 1 bathroom, but it has a fireplace! (If it's a working fireplace, that is really nice to have in Calgary winters.)
Listing ID: 68413 - Radisson SE, this is a townhouse with coin operated laundry. The place looks decent, a bit small, but the selling feature here is how close it is to the train station at Marlborough. You're right on 36 St and blocks away from the train. It's a good location if you need to commute downtown or anywhere outside of the SE/NE
Listing ID: 27957 - Vista Heights NE. This is the cheapest option I've seen so far at $1,095.00. I've been to Vista Heights to look at a place and they were basic, but nice. The rooms are small, but it has a playground on site. It's also not the best location as far as commuting, but a bus goes through here that will take you to the train.
Listing ID: 53153 - Penrooke Meadows SE. I have a friend that lives in this complex. The construction is basic, but safe. You can catch the #1 bus here on 52nd Ave to downtown (or transfer to the 305 bus once you get to 17th Ave for faster commute.) It's close to a lot of schools and the mall. Her neighbors all seem nice and my friend has no real compliants about the place (except it's small).
To stay within your budget, NE is the best option. You'll find places in the SE as well, but most of them will be in less desirable neighborhoods. Avoid Forest Lawn, Dover, Ogden, and the areas immediately surrounding them. (These are all in the SE.) If you happen to find a nice place to rent in Saddleridge, they are building a new train station to be opened soon there. Same goes for the SW, although house prices are much more expensive there. (I live in SW and pay $900 for a basement unit that is small. We could pay $750 for the same unit in the SE.... but the location is great.)
