George, Washington State and closeby

Mount Rainier National Park is between the amphitheatre and Seattle, so that stands out. You are at least a days drive from the classic "Canadian Rockies" around Banff, so I would skip that. Too many other interesting spots closer.

Weather should be dry and pleasant in early October IME.

Thanks Sam!

Check on new advance-booking rules for some National Parks, maybe less severe in October.

Wow, with that much time, you certainly could go quite a few places. Don’t let yourself get discouraged if going to Canada is a top priority. I think that is my main question before making recommendations. What interests you? National Parks? Hiking? Biking? Wineries? History? How much would you want to drive In a given day?

The state of Washington has two distinct zones in terms of weather with the Cascade Mountains separating the two zones. The West side of the state tends to be the wetter side with cooler temps in summer and warmer temps in winter. The East side is drier with far less trees. October weather will be different in each zone.

Depending on how much of the Canadian Rockies you feel the need to see, if driving to Banff is too much you could instead go to Glacier NP in Montana and then drive to Waterton Lakes NP (Canada). Both of these are beautiful and most years the weather is cool but nice in the first half of October. The Rockies there are beautiful though maybe not quite as dramatic as farther north. You could also make a visit to the Octoberfest in Leavenworth, WA. Also the whole Columbia Gorge between WA and OR is lovely in October - I think Oct is the best month in Oregon and assume WA is also nice then alghouh I've only been to Seattle in October. Another area of WA that is beautiful is the Olympic Peninsula and maybe even a ferry to Victoria, BC, Canada or just a cruise through the San Juan Islands. Beautiful area you're visiting.

And by the way, I did check and the National Parks do not require timed reservations in October so visiting them should be a breeze and definitely not as crowded as during the 'season'.

Air NZ has nonstops to Vancouver from Auckland. Otherwise with a connection in San Francisco.

October will be apple season in Wenatchee and Yakima. Great places to visit are Lake Chelan (ferryboat to the end) and the North Cascades NP (more of a drive through, but great hiking). Wenatchee is close to both Lake Chelan and Leavenworth.
On the west side of WA is the San Juan Islands and Puget Sound.

Where you enter/depart North America, does influence what destinations are feasible and an order of travel

Having the concert in the middle of your time here does put some constraints on how far you can go without having to be in a rush.

You accustomed to driving on the right side of the road?

Early Oct is a good time, weatherwise, to be here. East of the Cascade Mountains 70sF to 80F; West of the mountains mid 60s to lower 70s, would be typical. ( That would be the fat part of the bell curve)

1462churchill,
If you are in the area of the Olympic Peninsula, within the Olympic National Park are four temperate rain forests. The largest is the Hoh. Also the Quinalt, Queets and Bogachiel. They are magnificent and lush, well worth a drive. We drove through the Hoh on our journey to Port Angelus, where we spent the night before taking a ferry to BC early the next day. You might want to factor in a day in one of the rain forests while in Washington.

The rain forests are not at their lush best in October, unfortunately, and Olympic National Park is a long drive from George—-7-8 hours at best. The other 2 Washington national parks, Mt. Rainier and North Cascades NP, are much closer, and should be very nice in early October.

There isn’t really any place to stay in George; the one time we went to a concert at the Gorge we booked a room in Cle Elum for after the concert. It took 2 hours to get out of the parking lot after the concert, but I hope traffic control has improved since then. A closer place to stay would be Wenatchee, 40 miles from George, and there you would be well-positioned to head north into Canada or north to North Cascades NP.

For the latter, I suggest you stay at the remote North Cascades Lodge at Stehekin, reached by boat up Lake Chelan from the town of Chelan (close to Wenatchee). This is the only lodge that is actually IN North Cascades National Park. 2 nights there would be sufficient.

https://lodgeatstehekin.com/

From Chelan you could continue north to the little faux Western town of Winthrop, in the Methow Valley. The town and surrounding area offer good lodging options and some good restaurants. This is one of the gateway communities for North Cascades National Park. This is really a hiker’s park—-you pretty much have to hike to get into the park itself, but the scenery from the North Cascades Highway corridor is beautiful as well.

One of our favorite autumn hikes is just up the highway from the Methow Valley, at Rainy Pass. It is a section of the Pacific Crest Trail, which runs from the Mexican border with California up through Oregon and Washington to Canada. In autumn you will likely meet some through-hikers who are nearing the completion of their long trek. Congratulate them.

https://www.wta.org/go-hiking/hikes/cutthroat-pass-via-pacific-crest-trail
(That lead photo was probably taken later in October, when the larches turn golden).

Lodging, events and activities around Winthrop:

https://winthropwashington.com/

You have 2 separated time slots, before and after the concert on Oct. 4. It would work to use one for the North Cascades as I suggest above, and the other for Canada. The Canadian Rockies are pretty far to the east, but you could do a nice loop straight north to Harrison Hot Springs, and then west to Vancouver, maybe visiting Whistler for some outdoor activities

https://www.harrisonecotours.com/

https://www.whistler.com/activities/summer/

There has been no response from the OP. I suggest we wait for further suggestions until we know what their preferences really are. No purpose in just throwing things out without more information. To clarify some of the other posts made previously.
1. There is other lodging in Stehekin, The Stehekin Valley Ranch, but it closes at the end of September.

2. In my opinion, Leavenworth will always disappoint anyone who has actually seen a real Bavarian Village.
3. October is a good time to go to Olympic National Park. True the rainforests don't look the same as in Feb or March, but they are still good and the lack of crowds make up for it.

I wouldn’t recommend Leavenworth to anyone under the age of 60, especially if they are interested in outdoor activities. The hiking there is not nearly as good as the hiking from highway 20 (North Cascades Highway). The one hike that might be good, Colchuck Lake, has been ruined by Instagram fame.

Lola’s advice is spot on. I would listen to her.

I recommend the novels of David Guterson set in the area and subsequent movies:

Snow falling on cedars
East of the mountains

To give you a different viewpoint on the area

Excellent suggestions, Lola, for some beautiful spots!

I agree, Lolas advice is good.

Just to clarify another reply, it is highway 20 that is the North Cascades Highway, not 30.

Stehekin is a wonderful place. We always opt for privately owned cabins instead of the lodge there. Some of the owners have vehicles for your use, which is really nice.

ONP is wonderful, especially in the fall.

If you add in the Rockies, I would do those first just due to weather.

OP has not returned. I'm not sure that we are even close to meeting what they are interested in without more input from them.

Oops! Of course I meant Hwy 20. Typing on my phone it is easy to make a mistake by adjacent numbers. I will correct that.

We are having a fun conversation in any case. Maybe the OP is busy with work or something. But it would be nice to get some feedback on the ideas so far.

Sasha--Oh my gosh yes, on the phone it is so easy to do that!

Thanks for all your replies! We have booked flights into Calgary, we stay 1 night then pick up an RV. We have approx 5 days to get to George for the concert, and I have booked camping for the ampitheatre. We enjoy hiking, biking, horse riding, farming, the western lifestyle and I would love to see as much wildlife as possible. We will then have another 6 days to get back to Calgary and want to find an interesting loop. We would love to book a trail ride in the Rockies but want an authentic as possible experience as we are all confident riders.
Thanks for any more ideas you may have!

Flying to Calgary is a whole different situation for logistics. All the prior suggestions are good ones if you had flown into Seattle from the start; apply those to your post-concert travel. I'd suggest focusing on a route through Montana/N. Idaho on your way to George. There are forum members expert on those locations. Currently one main road from Calgary (BC 3) has construction closures (may not be an issue in October). It's a big long drive regardless, 4-5 days is not much time out that way. Eastern Washington is high desert, prepare for cool nights, weather could be decent but not hot. Depending on how the fire season goes, it could be smoky (can't predict that at this point). Also you're going to change time zones on that route, make sure to adjust your watch.

Thanks for the update and giving the information that is necessary to give you better answers. Knowing that you are flying in and out of Calgary changes everything.

Here is one idea for a loop route-- I suspect others will have better ideas, but this gives you a start and a general idea of travel time. Depending on how big the RV you have, adding closer to 20% , vs 10% to the time estimates may be, advisable.

https://www.google.com/maps/dir/Calgary,+AB,+Canada/Banff,+AB,+Canada/Kelowna,+BC,+Canada/George,+Washington/Glacier+National+Park,+Montana/Calgary,+AB,+Canada/@49.6395318,-123.0208404,6z/data=!4m38!4m37!1m5!1m1!1s0x537170039f843fd5:0x266d3bb1b652b63a!2m2!1d-114.0718831!2d51.0447331!1m5!1m1!1s0x5370ca45910c4afd:0xcaafaebedaac9463!2m2!1d-115.5707903!2d51.1784304!1m5!1m1!1s0x537d8cb6e3c730b3:0x4ef8e53ddab4c4f7!2m2!1d-119.4965917!2d49.8863235!1m5!1m1!1s0x5499753251ef4209:0x4e5c829163ee7e92!2m2!1d-119.8558822!2d47.0790224!1m5!1m1!1s0x5368901555555555:0xaf16bc2215c55dec!2m2!1d-113.7870225!2d48.7596128!1m5!1m1!1s0x537170039f843fd5:0x266d3bb1b652b63a!2m2!1d-114.0718831!2d51.0447331!3e0?entry=ttu

What side trips you do will depend on what interests you. No clue about horseback rides.

I would probably go counter-clockwise. The later into Oct it gets the better the chance of inclement weather at the higher elevations.

$0.02 fee waived.

Happy travels

I really like Joe32's route. One diversion would be north of George, by Colville head west up Hwy 20 a bit to Winthrop and Mazama area. Some great hiking around there in the North Cascades. Probably not enough time to do, but the drive across Hwy 20 is beautiful, but would be slow in an RV. And that time of year they do get snow in the higher elevations and the pass across to the west closes for the season usually around November. You will have an amazing and beautiful adventure! So many highlights to see!