It’s been nearly a year since I lived in Edmonton, but I don’t imagine things have changed that much.
I lived near the University of Alberta, which meant that I lived near Whyte Avenue and Old Strathcona. That is the place for nightlife; while there are many nightspots in Edmonton, there is a concentration of them on Whyte Avenue. So you would probably find it a good place to go, since if you find you don’t like the place you’re in, you can go a few doors down the street to another. I wasn’t a nightclubber, but I did pop into O’Byrne’s a few times. O’Byrne’s is an Irish pub with a young crowd; it’s on Whyte Avenue between (IIRC) 106th and 107th Streets. And although it’s not on Whyte Avenue, Hudson’s (87th Avenue, between 111 and 112 Streets) is where you’ll find a lot of people about your age–they’re all university students and in their early 20s. As you might expect, Hudson’s is packed on Friday and Saturday nights, but pretty much every night, it gets busy. They have something every night (DJ, drink specials, etc.), and the party is usually best in the basement. As you might be able to tell, I’ve had more than a few drinks there; but then, I lived just around the corner. 
You tell us that you’ll be staying near West Edmonton Mall and you’ll be taking public transit. To go to Whyte Avenue from there, take the Number 4 bus from West Edmonton Mall. The bus will head for the University Transit Centre; stay on the bus when it stops at the University and when it gets going again, it will head for (and then along) Whyte Avenue. You can reverse the process to get back to West Edmonton Mall, but if it is late at night, I’d recommend a taxi. You’re pretty safe on the bus, but waiting at a bus stop late at night may not be something two young women would want to do.
Public transit in Edmonton does get you where you are going–eventually. Service is good in rush hours; at off-peak times (especially nights) and weekends, service is poor. Buses and LRT trains run infrequently outside of rush hour, and it is not uncommon for some buses to be scheduled every 30 minutes at these times. So if you miss one, you’re stuck waiting up to a half-hour for the next. For this reason (and especially if you want to hit Whyte Avenue), you’ll want to have the number of a cab company (or two) handy. Cabs are very good at hanging around where they’re likely to be needed, pubs and bars are always happy to call one for you, and of course, you can always hail one on the street; but if any of these don’t result in a cab, you’ll want a cab company’s number so you can call one yourself.
That’s about all I can think of for now. Not living there anymore, I’m unsure what concerts/bands/festivals/etc. might be going on, but maybe a real Edmontonian is up-to-date on those things. Have fun!