Hi Paul, my daughter and I were in Iceland last month - we used the Lonely Planet Iceland guide to find most of our lodgings, but I'm not sure what you'll be able to find for under 80 euros a night. Iceland was expensive! We rented a car from Dollar, stayed in an apartment in Reykjavik for two nights, then drove along the Southern Coast for two nights, staying outside Vik at a cottage on the black sand beach at Reynisfjara, then drove up to the northernmost town in Iceland, Siglufjordur, where we stayed at Siglunes Guesthouse, and stayed on the West side one night in Borgarnes, where we had a studio apartment. I looked hard for budget accommodations - we paid around $170 per night for each of these. I can give you more details about these places if you are interested. We looked for places with kitchens and ate breakfast and some dinners in our apartment to save money.
As for activities and things to see, we loved driving along the South coast - the landscape changes quite a bit as you drive along and there are tons of waterfalls, sheep, black lava fields, even glaciers that you can see from the car. The black sand beach and basalt columns at Reynisfjara were one of my favorite stops - puffins nest on the cliffs above the beach. There is a parking lot from which you can see the beach and columns, if you want to get right onto the beach there would be just a bit of walking involved from the parking lot to the beach, but it is all flat if that helps. The glacier lagoon, about two hours further along the Ring Road from Vik, is also beautiful, but we used a side parking lot, not the main one, so had to walk over a small hill from the parking lot to see the lagoon. I know they do boat tours from the main parking lot, so I imagine that would be easier for your wife.
My daughter and I also drove along the Ring Road to the North side - and the scenery there is amazing as well. Iceland is actually a great country for driving - we drove for three hours one day and only saw two other cars - and the scenery is beautiful so even if you can't get out and hike, you can still experience much of the beauty of the country. We loved the little town of Siglufjordur, we went up there to see the Midnight sun, but the town itself is cute and has a nice little marina with a couple of really good restaurants.
Borgarnes also has a nice museum - the Settlement Center - which we quite enjoyed. We only were here for one night so didn't get to explore too much.
Hope this helps! Have a great trip!!