Cathy, that sounds like a great trip!
It has been a long time since I was in the Black Hills of South Dakota. I lived in Spearfish and worked out of Deadwood in the summer of 1978 between my junior and senior years of college (majoring in forestry). We spent every weekend climbing. The needles of South Dakota are amazing and I really encourage you to drive the needles highway. It has some tunnels that are "interesting" It is fun to watch a tour bus make it through them.
One of the highlights of that summer was climbing Devil's Tower. It is a pretty amazing geological formation and I think it is really worth a slight detour to check it out.
Much of the Black Hills is very touristy (as Kevin knows from his wagon wheel experience)!
Overall, I found Spearfish boring, Mt Rushmore interesting for an hour, and the needles to be fascinating beyond belief!
Things have certainly changed over the last 40 years. I was there before Deadwood had legal gambling. From what I have read, it is a very different town now and one that I would go out of my way to avoid (gambling and the circus that surrounds it is just not my thing).
The whole area has amazing natural beauty. You really can't go wrong.
As for Yellowstone. May will be early and it is likely the Beartooth highway will not be open in time for your trip. You might be able to enter the park through Cody WY, but even that takes you over Sylvan Pass, which is closed early in the season (May and June are "early"). Your safest, but least scenic bet, is to stay on I 90 all the way to Livingston and then turn south to enter through the north entrance at Mammoth. Note that Mammoth is much lower in elevation, so it is open year round.
The main road in the park is organized as a figure 8. Unfortunately, one of the key legs of that will be closed for all of 2021 (for construction). That is the route from Tower to Canyon over Dunraven Pass. That is too bad, as it really makes it take a lot longer to get around the park.
To me, there are 3 kinds of activities worth pursuing in Yellowstone. First and foremost are the thermal features. For this, I recommend the old faithful area. There are miles of boardwalks and hundreds of thermal features (the largest collection in the world, by far). It is pretty accessible by wheelchair, but is far from ADA compliant. With a capable wheelchair and a bit of patience, you can go many, many places. Don't just do Old Faithful. Do the boardwalks behind Old Faithful all the way out to Morning Glory hot spring (technically a geyser). Do it at different times of the day. If you see folks with walkie talkie radios, they are probably more serious geyser gazers. Ask them if they have suggestions for geysers that are close to erupting. It is worth the wait to watch Grand geyser erupt. You can find predictions at
www.geysertimes.org. Be aware that cell phone coverage is not sufficient to be able to use that website while you are in the park. They have an app that you can download that will cache the predictions. It runs on android and IOS devices. Cell phone coverage is sufficient to periodically update the cache of predictions.
The other geyser basis are also worth visiting, especially Black Sands, Biscuit Basin, Midway, and Norris. West Thumb is also worth a visit, but is more about natural beauty than thermal activity.
The second main activity is wildlife. Going in May is wonderful for wildlife. I highly recommend the Lamar Valley and they Hayden Valley for wildlife viewing. Bring binoculars. If you have it, bring a spotting scope and tripod. I can sit for hours at the Grizzly overlook in the Hayden valley looking through the spotting scope. If you don't have a spotting scope, others are usually willing to let you look through theirs, though they may be set up in a place a wheelchair cannot reach.
The best places for wolves are the Lamar Valley and the Grizzly overlook area of the Hayden valley. I have had good look watching bears in the Lamar Valley, Hayden Valley, and especially along the stretch between Fishing Bridge and Sylvan Pass. Black bears can be common around Tower, but I don't know if the road will be open to it (due to construction).
The third reason I like to go to Yellowstone is the natural beauty of the area. We spend hours and hours just driving around looking at the beautiful sights and occasionally stumble across some wildlife.
I also recommend a trip down to the Tetons. They are beautiful and there is a wonderful bike path that is GREAT for a wheelchair. It is one of my favorite places to take a long ride.
You have probably already discovered that getting lodging inside the park requires booking well in advances (9 months to a year). Getting a May reservation in the Old Faithful area will be problematic. The Old Faithful Inn does not even open until June 4 this year. There are 2 other lodges in the Old Faithful area, so check them for availability. Note that there are no true ADA accessible rooms, but I have made one of the more expensive rooms at the Old Faithful Inn work for me. There is a communal ADA shower on the first floor of the Old Faithful Inn that I can use (very large, with a roll in shower).
I have taken many pictures of Yellowstone over the years. Those are posted on a website at swalkeratvail dot zenfolio dot com. Most of the pictures have the location. Reviewing those will give you an idea of where wildlife hangs out in the park.
There is too much in Yellowstone to see and do in a single trip. I recommend picking a few things and doing them well. If I had to choose, I would plan on doing the Old Faithful area well. It is unique in the world and is an absolutely amazing place. I would also plan a day driving the lower loop (Old Faithful, Norris, Canyon, Hayden Valley, Fishing Bridge, and West Thumb. I would plan another day in the Lamar Valley. Note that the drives are long (longer with Dunraven Pass being closed). I would also spend a day in the Tetons. Wildlife is typically out at dawn and dusk, though bears will be out whenever they feel like it!
Ask as many questions as you like. I will be glad to share whatever information I have.
Steve