Inspite of living in Edmonton for over 6 years, I still do not know all the neighbourhoods and probably still would not be able to tell you if you mentioned one if it's good or bad unless I'd lived there. It can also vary a lot within neighbourhoods, even over a couple of blocks. It is also quite different what is safe for a single guy vs. what is safe for a woman who might be around by herself or what is safe for kids.
Your biggest indicators when you go to look for apartments is to look at the shape of the neighbourhood and look at the people around there and then ask. Do not bother ask the landlord because he is going to tell you it's awesome and perfectly safe but ask neighbours, ask people on the street and number one ask the people who work around there in the convenience stores and gas stations. They have to go home after their shift is over so they would be the best to tell you if they feel safe going home at night. If you already see that the neighbourhood is full of ppl who look like hookers and drug dealers and the houses are run down, then of course you don't have to ask :) Do not rent a place over the internet unseen.
Be careful of the landlords, even if your English is perfect, there are a lot of shady landlords out there and better to put everything in writing. Make sure you do a walkthrough before you move in and all damages to the apartment are listed on there. Make sure you get a copy of your lease and your walkthrough report. Document the damages with photos. Take a place with onsite management rather than not. It is a lot easier if you end up having loud neighbours to get the manager to witness the noise than if you have to leave a message on the landlords office answering machine who may or may not deal with it the next day. If you have to complain about something to the landlord, document it. When you move out, document again the state of the apartment with photos. The landlord will probably do a walkthrough and if the walkthrough report is listing something you didn't cause or something that was on the walk in, refuse to sign it. In any case make sure you get a copy of the walk through again. Landlords in AB may request a 1 months rent damage deposit and it's rare to get it back because the law is basically on their side so just be prepared in advance that you may have to fight for it. They can basically invent damages that weren't there or blame you for stuff that was already there when you moved in and they do not have to show you any receipts for anything they had to fix for why they are withholding your DD, if they do it, as long as you didn't sign the walkout, you can take them to the tenants board, otherwise you have to sue them.
Not much difference from here in Atlanta :-D