Two couples are spending 3 1/2 days in Yellowstone NP, 2 1/2 days in Grand Teton NP, next September. We have a pretty good list of what sights to see - the question is how to see them, and what is the best way to experience the parks? Are their park tours for which we need to/should sign up in advance? Is that the proper amount of time for each park? (We already have hotel reservations). We are all in good health, but in our mid-70s, are there hikes we need to take? Any tips appreciated. Thanking respondents in advance...

That's a little short for Yellowstone--it's huge!
Last September I spent a week in Yellowstone and 3 nights/2 days in Grand Teton and thought that was about right. Check for ranger-led walks/hikes in Yellowstone, we enjoyed a number of them.

One thing that caught me by surprise--all of Yellowstone is above 7000 ft. I tried to do a hike the day after we got there and ended up with a headache.

Enjoy your trip, it's an absolutely beautiful area.

What is your list of what you want to see? If you publish that, then people can help you piece it together. You don't need to do tours--you can see this all on your own. Have you checked out the NPS website for info on both parks? Has info on the hikes, itineraries, etc. What is your experience with altitude?

Definitely allow yourself time in Yellowstone to see as many of the thermal areas as possible. The walkways around these are easy and this is really what Yellowstone is all about because the thermal activity is truly unique. Stay inside the park if at all possible. We love staying in the Old Faithful area, with the Old Faithful Inn as first choice, but other lodgings there are OK, too. Plan on spending a good deal of time in the car each day driving from place to place. You can't see it all, so just do a little research and see what attracts you most. The only tour we did was the boat one of the lake, which I found a little boring.

Some highlights in the Tetons you may want to consider:
The drive along the Moose-Wilson Road corridor - be advised it's not paved and can be a little bumpy, but it's a great area to see wildlife (moose mostly).
Dornan's near Moose Junction in the park - the must-stop place in the park to get something to eat, great little grocery/snack store, chuckwagon dinners, etc.
For amazing photos and an opportunity to see swans - Oxbow Bend. You just park in the lot and the amazing scenery is right in front of you.
Jenny Lake - take the boat trip across Jenny Lake
Baker-Ewing Float Trip - we did this a few years back and saw at least a half dozen bald eagle: http://www.barkerewing.com/
For some beautiful lake photos- Phelps Lake early in the morning
Mormon Row drive - this is where you'll recognize the famous photo of the barn in the forefront of the tetons - great spot for photographers
Lots of historical structures on the drive around the park (Cunningham Cabin, Chapel of the Sacred Heart, Menors Ferry)
For some shorter beautiful hikes/views: Sring Lake, Lunch Tree Hill, Inspiration Point: Best Easy Hikes in Grand Tetons National Park

Enjoy your trip. September is a beautiful time to visit!