We are thinking of visiting some time late spring to early summer and wondering if anyone has any suggestions on how to get there from the Phoenix airport and how to get around once we are there without renting a car. A car rental for 3 weeks is ~ $ 1,600 for 3 weeks and that seems like a lot when the car would remain parked most of that time.
I checked into shuttles and the quote I got was ~ $ 120 one way but that doesn't help with quick trips to the grocery store or maybe a couple of runs to Phoenix to catch a movie etc.

We have visited the resort many times but not stayed there. It has a nice pool, the entire property is not overly large but other than the pool not a lot there, a multi purpose room etc.

The place is a bit isolated north of Cave Creek which itself it north of Scottsdale. There is nothing walking distance and I think you would feel very isolated without a car - i don't recall much if any dining at the resort but that might have changed.

I would rent a car absolutely.

We were there last year and it is isolated but great for getting away from the hustle of the city but with nice pools, nude all day and night and there are some limited restaraunt offerings.
We rented a small cabin that came with a mini kitchen so cooked most of our own meals.
There are some on - site hiking trails which became a morning ritual. I also found a reasonably well equiped work out room with weights and some tread mills.

Have been there a number of times for the day and a few times stayed multiple nights. I can't imagine staying there and not having a car. The price you got for three weeks seems high. If you rent outside the airport it can be a better rate. Seems like if you rent at the airport for pickup the airport adds a charge, least use to be that way. I usually stay my first night and last night at a hotel that is near the airport that has shuttle service. I arrange to rent a car somewhere near the hotel and seem to get a better rate. Unless rates have really gone up I would think you should be able to get 3 weeks closer to $1200, still not cheap but a lot better than $1600.

I have to agree with those stating that a car is a must if you're looking to visit the market, Scottsdale and do any other exploring of the surrounding area.

I've visited twice and as I recall, there is a small shopping center about a mile or two from Shangri La Ranch but it is about a 40 min drive to Scottsdale.

It's a stretch and there are most likely legalities involved but maybe a call or email to Shangri La to see if anyone that resides at the Ranch has a car to rent? It may be worth the question.

Have a good time!

One thing to remember is that we are from Canada and for every US dollar we pay 1.4 Canadian dollars.
We went there last year and rented the same car dollar for dollar so nothing has changed except the dollar exchange.
Even the Shangi La fees are 40 % higher due to the dollar difference.
It makes for a 40 % higher cost vacation when travelling to the US this year than it was about a year ago.