Edmonton for the first time...
As moose has mentioned, Suede is good downtown. Fluid Lounge is on the corner of 109 street and Jasper Avenue and has a good martini'ish loungy kind of vibe.
During Fringe Fest, however, i'd recommend going down to Whyte Ave - thousands on thousands of pedestrian traffic, it's a great scene. On Whyte, Blue Sapphire (north side of Whyte just west of 104th Street) has a very martini/lounge kind of feel. Across the avenue is the Savoy, which is bit more artistic/bohemian, but has a great Vibe. DJ's spinning, lots of people enjoying, sipping, and relaxing. Im sure there are likely a few other places open now (as turnover is pretty high in some locations), so hopefully a resident can fill you in on the more recent comings and goings.
In terms of food, more details are required. But for me, can't misses for me in Edmonton include: NY Bagel Cafe and Culina for breakfast/brunch, Dadeo/Pagolac/Churros King, Spinelli's for a sandwich and a canoli for lunch, and Sofra, and a variety of fine dining restaurants (Hardware Grill, Blue Pear, Sage, Red Ox inn) for dinner.
If you're coming during August 16-26 a large chunk of the city's population will be at the Fringe Festival in Old Strathcona. There are lots of restaurants and bars in that area.
Downtown, my friends can't say enough good things about Suede Lounge.
If you give us an idea of your price ranges and preferred areas of town we could give you better restaurant recommendations.
Funny you should mention Suede Lounge. I dropped in for the first time Wednesday after work. I have driven past it many times but never had an occasion to stop. I was picking up some Lebanese food at Lashish around the corner so popped in while waiting for it to be prepared. Nice spot and it sprang to mind given dannyboy's descriptors.