Sure I can assist you with this. I don't live in banff anymore (now I'm on Vancouver Island), but I fished all over that place and loved every bit of it.
I will break down each area using numbers so you will know if I'm talking about the same area or am moving on.
Now mind you, the 'luck of catching fish' I keep talking about all depends on how many tourists are around because there usually is a few and it also depends on how fished these areas are. Usually, when fishing season opens anglers flock like crazy and fish them out right away.
1. Fishing Location
The best places to go in my opinion, and its best because these are where I actually caught most of the fish, is around by the Bow Falls, (upper and lower though I had more luck on the lower end). You'll know you're in the right area when you see the falls on the left and a golf court on the right from where the falls are located. There you'll see a green bridge that goes over the spray creek which is great fly fishing opportunities but may be closed for fishing depending on the season. You can drive over the bridge, or walk over if you prefer, I just usually parked my car just before the bridge and walked across because the fishing spots are pretty close by, and about 50 - 100 feet or so from the bridge on the other side will be what looks like a dirt 'parking lot' kinda thing. This is where they usually launch the rafting tours so you may see large red rafts in the area. If you do see them, then you know you're pretty close to the fishing spot. What you want to do is walk through the dirt parking lot area and find a trail that leads around the golf course to some large rocks (will be on the LEFT hand side as you walk), and you'll see the shoreline of the Bow River. I usually fished off the big rocks because there is a pool that forms there and I would cast in front of the largest rock and slowly reel in my fly or spoon and I usually had good luck catching nice sized browns there. This also depends on how many tourists are around and / or fishers because sometimes the area does get over-populated.
If it is over-populated, just follow the river shoreline (I say shoreline because if the river is at a 'normal' level, it will look like a shoreline.) all around the bend and there you'll find really sweet hot spots for fly fishing. Unless the river is high, I wouldnt attempt to use anything other than a fly or light weight lure (such as a light rapala) if you're spin casting because the river is usually pretty low in this area and snags can be a problem. If you have waders, as you walk around the bend you will see what looks like another river capillary or channel (sorry my brain is acting up and I cannot remember the true term), wade out towards the middle and fish where the two connect. You should see the seams. Usually a great place to fly fish.
2. Fishing location
Another great place to fish, either using lures or flies, is behind the golf course. Just go towards the falls as explained in #1 and continue driving over the green bridge you will see if you keep following the road and keep following the road all around the golf course. It's a really nice scenic drive as well. I usually enjoyed going to this spot which I found just by cruising around doing nothing. I just so happened to come across it and since I usually keep my fishing gear in my car for "emergency reasons" lol, I stopped and fished. I had really good luck here with browns and some rainbows. What you do is follow the road all around until you see what looks like a 'ditch' (which is actually the spray creek if I remember correctly), connecting to the main bow river. You'll have to park your car along side the road but thats ok cause you'll be pretty close. Fish the 'ditch' and seams where the two connect. You should have some pretty good luck here.
3. fishing location
Another great place to fly fish, if you have waders that is because this one will require them, is just below the traffic bridge going across the banff ave towards Canada House (you'll see it. It looks like a castle / mansion at the end of the ave.) You will have the option to be able to go left or right once you cross this bridge. (if you go left, you follow the road around and this is how you get to the Bow Falls I was talking about above.). In this instance, go right and then take the first immediate right and follow this down until you can find parking somewhere. Wade out to the middle of the river (if its low enough) and work your way down with the fly until you're just below the bridge. You will see breaks and mini-pools. This is where you'll most likely find the fish. And this is where you'll most likely be photographed the most. I can't tell you how many times I was photographed fly fishing by the tourists who where in awe of my casting abilities lol.
4. Fishing location
If you don't mind traveling abit, and for these next two, taking your sweety would be a bonus cause the locations are really beautiful if she's into nature stuff. Leave banff and get on the ole trans-can and head towards Lake Louise (I used to work in Lake Louise and I can tell you there's great fishing there two. Especially right outside right at Castle Junction for rainbows.), a few kilometers out of banff (I think it's like 2 - 4 but don't quote me on that), you will see a rest area (will be on your right) with a gate on the wildlife fence. Park your car and open that gate making sure to close it so wildlife dont get out lol, (yes it's legal to open the gates and go through them. Alot of people don't know that but it is.) and there you can fish the Bow in many, many wonderful areas. If you walk alongside the bank to the right, you will come across some really magnificant pools and they're usually holding some nice sized rainbows
5. Fishing Location
As mentioned above, castle junction is a fantastic place to fly fish. Great location, hot fishing spots (even as a traffic bridge you can fish under which produces results when the sun is hight), and just over-all a beautiful area. To get there you go as if you're going to Lake Louise. I cannot remember the exact location so you'll just have to follow the road signs.
6. Fishing Location
Last but not least if you really don't want to do alot of driving, you can always go back towards the park gate (the gates where you paid), and just before you leave, on the left hand side you will see a large parking area. You can park here, and on the side of the road if you wish, and walk that trail you see which will be on the right. That leads to some great spots in the river.
7. Fishing Location
Vermillion Lakes in Banff is a good spot to fly fish. I heard there were pike there from a Game Warden but I'm not sure.
8. Fishing Location
Lake Minnewanka is a great place. You can pull out some lunkers there. But it's really best if you have a boat. You can rent a boat there if you'd like. I fished here quite a bit and really enjoyed it.
Two Jack Lake. Another great place to fish. Along side it you will come across a channel where you can fish. I usually fished at the channel or the head of it.
That pretty much wraps up the placies I fished. I fished all over but for the most part these places were the bulk of my fishing ventures and the bow river is one of the best rivers I've fished. Just gotta find the sweet spot and that will usually be outside of banff if there's alot of tourists.
Taking a drive outside of banff going towards lake louise you will see many spots, like pools, eddies, seams etc and you can just pull your car over and fish. The spots I mentioned above is where guides usually take their tours or around those areas so you should have some luck.
Ahhh, those were the days, now since I'm on vancouver Island I heard this was the fly fishing capital of North America so now I need to find out if that's true or not. I'm going to hit up the rivers and streams in a couple weeks if possible
Hope this helps and I really hope you enjoy your vacation in Banff!