Fall trip to Canadian Rockies

discovering places that may be off the beaten path.

https://www.lakeohara.com/

Definitely outside of your stated price range BUT definitely worth the splurge - greatness comes at a cost.
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OR explore a day trip

https://parks.canada.ca/pn-np/bc/yoho/activ/randonnee-hike/ohara/visit

Unfortunately, rates for shoulder months or off-seasons are still up there when it comes to the Canada's mountain parks.

You could look at a stay at the Columbia Icefield enroute to Jasper

https://www.banffjaspercollection.com/hotels/glacier-view-lodge/

In Jasper I like to stay at either

https://www.jasper-park-lodge.com/

OR

https://alpinevillagejasper.com/

Oh, and by the way, there is a whole lot to see AND do along the Icefields Parkway

https://parks.canada.ca/pn-np/ab/banff/visit/les10-top10/glaciers-icefields

https://icefieldsparkway.com/
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Perfect example of your stated "discovering places that may be off the beaten path"

https://www.hikethecanadianrockies.com/hiking-trails/banff/parker-ridge

AND

https://www.hikethecanadianrockies.com/hiking-trails/jasper/wilcox-pass

We had a wonderful four day tour of the Canadian Rockies from Vancouver in late August with a firm called Key West Tours.

Here is their link
https://keywesttravelandtours.com/rocky-mountain-bus-tours/

The tour was very reasonable and first rate.

I have no idea where you are in your planning or ultimately what experiences you're hoping to get.

So, if your plan is to make your way to Banff, then onto Lake Louise - maybe even a little bit of Lake O'Hara before making your way up to Jasper and then returning on the same route which is absolutely fantastic because you can split the sights along the Icefields Parkway 1/2 on the way up and 1/2 on the way back.

Here's what I think you should look into and consider. Exiting the east gate of Banff National Park and driving past Canmore on the #1 Highway will be an exit to Kananaskis (Highway #40) - it's an incredible valley of multiple geologic and geographic features. Your destination will ultimately be through to Highway #3 at Coleman. You then turn east on Highway #3 driving to Highway 22x at which point you'll turn north through yet another incredible valley making your way to Calgary for your return home.

There's logistics involved, stay in Kananaskis Village or Coleman / Blairmore. In my mind this is a 1 1/2 to 2 day trip - but worth every minute of your time and a wonderful way to cap off your trip.

One of the challenges with your budget is that September is very much high season for the Rockies as that is when we get the fall colours there. I just took a look at Banff, and was ( again) shocked at the prices. So you will either need to up your budget, or pick your itinerary pretty carefully. I don't know if you will find some prices go down if you watch.
Couple of suggestions, Canmore is very close to Banff and prices may be better. I just looked at the Paintbox Lodge, that we like very much and it is more reasonable. They will book up quickly. Revelstoke also seems to have much better prices. We stayed in Revelstoke this year in October and it was lovely.
I agree with everyone that it is a lovely drive up the parkway. We like both Jasper and Banff, but it does look like you will pay a big premium to stay there. I think it is worth it, personally, but you may want to stay one less night.
If staying in Jasper, you may also want to consider reservations for dinner too, particularly if a Sunday.
One possible itinerary : Calgary- Canmore- Jasper- Kamloops- Revelstoke- Banff for a night, then Calgary.
I should add, that Calgary itself can be quite pretty in September if you want to stay a night, and hotels should be cheaper. Unless it snows of course :)

Thank you everyone, I appreciate your input. Your suggestions are the type of ideas I was wanting. Since I will need to increase our budget for accommodations, I may reduce the number of days for our trip. We definitely want to spend time in Banff and Jasper National Parks, and driving the Icefields Parkway is a must. For our days at Banff Park, I'm thinking accommodations in Canmore may be an idea worth considering? Any suggestions on how many nights to spend in each location? Thank you!

There are hostels at several places along the Icefield Parkway. Some of them have a private room option. Some are more primitive. You have to bring your own food, but I think they provide linens and some have a manager on site. I looked at this option, but the private rooms were already booked for our trip last year.

I may reduce the number of days for our trip.

Never like to hear that as an option for the Foothills and the Canadian Rockies.
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any suggestions on how many nights to spend in each location?

Driving up the Parkway will get you into Jasper townsite later in the day - so for me, that would be a minimum of 3 nights = 2 full days which may be the minimum number of nights at some of the lodging options you look at for your stay, anyway.
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I've never been a big fan of staying in Canmore , Banff is what you came to see - see if you can make the townsite an affordable option.
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As for Lake Louise, if you're changing spots, take a look here

https://www.basecampresorts.com/bakercreek
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The Johnson Canyon Hike for me, is only a great hike if you go to the Inkpots.

You might want to check out Bear Hill Lodge in Jasper. I just took a look at it's prices in September and it is closer to your price range. It is a nice grouping of cabins in the townsite, which is nice for being able to walk to Restaurants in town.

Another spot to consider is Field BC. Very small little railway town. There is only one accomodation in town the Truffle Pig Lodge. With a fabulous restaurant. Rooms book up quickly as it is a good price. But you will hear trains. Emerald Lake Lodge is also near there and is lovely, but pricier. Might be worth it though. Even if you don't stay there, there is a nice 5 km walk around the lake.

Many of the "must see" hikes in Banff and Lake Louise, have become very crowded, particularly at that time of year, people trying to see larches etc. I would include Johnson's canyon in that, as well as Moraine Lake or Lake Louise itself. But there are tons of other hikes to find.

In terms of length of time to stay anywhere, if you do 10 days I would do something like this :
Canmore 2 nights ( it is close to Calgary, if your flight is late, and there are nice walks in town if you want flat, or up to Grassy Lakes
Jasper 3-4 nights, take your time going up the parkway, and there are nice walks/hikes close to town
Back down the parkway, maybe to Field/ Emerald Lake for 2 nights or Lake Louise
Last 2 nights in Banff

That would give you 10 nights, with longer you can branch out to Revelstoke, or loop from Jasper to kamloops and back You could easily drive farther in 10 days, depends on your priority

We stayed in our travel trailer, but we did our first two nights at Banff, the next three at Lake Louise (went to Yoho area one of those days to hike and explore and eat at the Truffle Pigs), three more nights at Jasper and our last night back at Banff. I thought that was a nice amount of time in each area.

This place caught my eye when we were in Jasper. I don't know the rates, but bookings for 2024 open tomorrow.

We had friends that saved money by staying in Canmore and Hinton. I think Canmore is a fine option, but Hinton would is too far away from Jasper for me to consider.

More great suggestions from everyone, so thank you! Budget has been increased and Alpine Village booked. Now for Banff or Canmore. I appreciate your input!

Before starting your incredible drive north on the Parkway, maybe make a stop a Laggan's Bakery in Lake Louise to pick-up some stuff for a picnic lunch at Bow Lake. There is a picnic pull-over just ahead of the entrance to The Lodge at Bow Lake (formerly known as Num-Ti-Jah Lodge) - nothing like the landscape - Bow Lake, the Bow Glacier above the Lake, Crowfoot Mountain, and the red-roofed Lodge across the Lake. I think the Lodge also has takeaway food but I haven't been there since the renovations so can't be sure.