In town, you might check out some stocked ponds in a park named for a monk's place of residence.
Access is tricky, and the species are definitely non-traditional, but there's a northern river close by that you can't spell without "catch". Not a great stretch, but it's there.
There's also a river named for a long fish. It has pike and walleye as far as my experience goes, but trouts were either nonexistent or hiding.
If you've the time, though, I'd head to the river named for Robin Hood's tool or the Scottish-sounding one near Ed's son.
As for guide services, Get Hooked is the one I remember.
I'm from Calgary, a few hours South of Edmonton, so not directly familiar with the offering in the Edmonton area.
Although this CBC news article is a few years old, it provides a good summary of the opportunities in the area.
Unfortunately, Edmonton is a ways from the Rockies and the river fishing will be warm water species like Walleye, pike, etc. There will be great public access, bike trails, etc. to the N. Saskatchewan River in the city of Edmonton. As Jake mentioned, you're going to have to travel 2 to 3 hours West to get to trout streams.
Alberta Fishing Regulations - Alberta allows the use of 3 hooks on a fly line. Dry - dropper is commonly used. We're the only province in Western Canada that still allows the use of barbed hooks. There are no Provincial restrictions to on felt soles on wading boots. Similar to Yellowstone NP, felt soles are banned our western National Parks (Banff & Jasper). The National Parks have separate fishing regulations as well.
I was completely amazed at how far the Rockies are from Edmonton (unlike Calgary), seemed to take forever to get to Jasper form there (about 4 hours if I recollect), so if you only have a few hours to kill, it will be warm water species. You may be there in the heat of an Edmonton NHL playoff run, could be electric.