I skied there one day as part of a Chamonix trip. Stayed in Airbnb in Chamonix. Drove thru the tunnel in the morning, it was quick. I didn't know this at the time, but Courmayeur is like a fancy type place - I think it's like the Aspen of that region. I did however have a great day skiing...I was with my wife and there was a lot of great intermediate terrain with some fun more challenging stuff to ski where she could just wait on the groomed runs at the bottom and watch me come down. On mountain "Refugio" food was awesome. Trip report I did which included pics, it was in February 2018.
Don't have much advice on lodging, aside from I recall Airbnb having many choices, but seems you checked that. I have a feeling it would be expensive for lodging in that area, but maybe look more into the Aosta valley a couple towns over and maybe find something cheaper?
Skiing is not a sport, it is a way of life.