Personally, I enjoy Avon/Vail/BC. But I have usually stayed in Avon/BC. Around Avon/BC, I have stayed at the Westin RiverFront (going there next weekend) , Sheraton Mtn. Vista (next summer), Falcon Point (Summer '21), St James Place, Poste Montane, Christy Lodge and a few in Vail as well. I find the town of Avon and Vail Village to be very walkable. There are some nice easy trail in Beaver Creek. And the walking/bike path along the Eagle River is paved. Vail is a short drive away if you want to visit there. Glenwood Springs is about an 1 hour west. Breckenridge is a bit over 1 hour east if you want to visit. Steamboat is about 2 hours away. There are wineries in Palisade, about 1 hour past Glenwood. So, Avon/Vail/BC, IMO, would be a good base for exploring.
I do like Breckenridge and Steamboat. (Been to Breckenridge about 4 times this year so far) But with the mobility issues that you described, and with Breckenridge being above 9000', I'm not sure that would be an ideal spot. (Vail/BC/Avon is around 8000')
I have stayed in Steamboat as well. And it is a very nice town and a bit more town like than Vail. I'm not sure if the day-trip options are as good.
Most of the resorts in the Vail Valley are good. I found Falcon Point and Christy Lodge to be a bit less nice than the Marriott/Westin/Sheraton. Also, if you go in the summer, be aware that some of the older timeshares may not have AC. Probably not an issue in the Spring or Fall.