Beth, some are better than others. I too have a disability which severely restricts my walking. First, and most important... Do you have a permit to park in spots for disabled? If you do, bring it with you. It will be honoured all over North America.
Recently I learned that at the Grand Canyon you are able to drive rather than take the bus, if you have the permit. Make further enquiries to confirm that. Besides that, many of the viewpoints are right by the parking area or the road, especially along Desert View Drive - AZ-64. Nothing quite like standing on the rim of this great natural wonder.
In Yosemite you can enjoy almost all of it from the car... it is a spectacular place, even if you cannot go hiking. Similarly in Death Valley - definitely not to be missed. Both parks have lots of roads all of which take you to different scenic areas. You could drive around in each of them for hours.
Zion has a shuttle bus to take you around... however it is best enjoyed walking some of the short walks... which for me are now getting too long. The river walk is wonderful if you can manage it. I did that a decade ago. Bryce is easily seen without any hiking. All the view points which look over the canyon are right by the road.
Canyonlands requires several short walks from where you park and in Arches you can see quite a bit from the car and the parking areas. (If I were going to drop any, it would be these two - they are more difficult to see.) The drive between Arches and Bryce - UT-12 is a spectacularly scenic drive.
Monument Valley can be seen from the car. Even if you don't do the tour on the tribal lands... it is simply stunning to just drive the roads in south eastern UT/north easter Arizona, such as US-162, US-163 and US-191 (you can see those routes in an atlas, as suggested above). Those routes will have you wanting to stop and take another photo every mile or so.
I'd seriously suggest you plan to include some, if not all the southern Utah national parks in your loop. From LV you could drive through Death Valley and Yosemite then to either SF or Monterey and down the Pacific Coast Highway (a 2 day drive) back to LA.
You won't see anything like southern UT and northern AZ at home.
Don't assume this trip will be your only chance. I did not hit the road until I had my seniors card, after rearing five children, and have just completed my seventh trip. You don't know what lies ahead of you.
Lifey
[p.s.Just got an alert from Trip Advisor for flights from MEL to Florida for $1600.]