We have 8 days, going in May with a person with some bad knees. What would your dream itinerary look like??
This is the condensed version of what we did in September when we had 7 full days.
Pick up rental car at airport and head to Reykjavik and stay there that first night.
Drive to Stikkisholmur and stay there. See the sights on the way up. Drive back down the next day to the Golden Circle with stops at places such as Helgafell (fine with bad knees),, Hvammsvik, Thingvellir, Bruarfoss etc. We stayed in Reykholt in this area.
Next day Golden Circle sites, Hrunalaug, Fridheimer for lunch. We did some big hikes after that so I will leave that out here since that would not be an option for you. Slept in Vik that night.
Next day was Reynisfjara, Yoda Cave, zodiac boat ride at Jokulsarlon, Diamond Beach, and slept near Hofn.
Following day we headed back south. Stopped at random places including Skull Beans in Vik, Kvernufoss, Skogafoss, Seljalandsfoss etc. Stayed at Hotel Eldhestar near Selfoss.
On that last day we rode horses and just did some random stuff. Our flight was that evening so we had the whole day.
You have a good reply, but it's not clear about the bad knees. Which is harder, walking around, or getting in and out of the car. Is level walking but on gravel or uneven paving stones worse than walking on a grass meadow? Is any hillside trail out of the question? Just one example, Thingvellir National Park is a particular highlight, and I consider the walking "easy", but there is a GREAT DEAL of walking. I wonder if you can book a ranger to meet you and some others with a golf cart for the return to the parking lot? (just asking, no idea. The point is that it's a well-staffed, large attraction.)
Snæfellsnes Peninsula, South Coast, and Golden Circle are the absolute musts, and any of them could be programmed for two days instead of just one full day. Note that room bookings must be made well in advance, probably advance pay and no refunds. I guess bad knees would particularly want a hot mineral springs soak.
Yes, hotels need to be booked quite far in advance. Most places book out 9-12 months in advance. We have only had nonrefundable rooms maybe in 3 hotels out of 7 trips, to give you an idea. We very rarely pay in advance as well.
As for Thingvellir, yes there is a lot of walking if you park once and then walk. However, there are quite a few parking lots, so you can make that work in your favor.