If you think in terms of nights in a place, and not days, are you thinking of 3 nights in Reykjavik and 3 nights elsewhere?
It's hard for me to answer your question directly since I have not been to Akureyri, although I totally understand why you want to go there. My answer addresses if you go south. No matter which, you might consider 2 nights for Reykjavik and add the other night elsewhere. It's an interesting city, but there is so much to see beyond there.
We went up the west coast and inland a bit for 2 nights, then stayed in Selfoss for one night and went out along the south coast to near Kirkjubaejarklauster. If you decide to go south rather than north, I would encourage you to go further along the south coast than Selfoss--towards Vik or Kirkjubaejarklauster. If you have the Rick Steves Iceland book, he describes many points of interest, beauty, and hikes along there. We did a glacier hike, went up Droholey Promontory for some gorgeous views, visited the black sand beaches of Vik, did a zodiac boat ride in the iceberg lagoon of Jokulsarlon, visited Vatnajokull National Park and did a moderate hike to a waterfall, along with other suggested sights. (And we are of similar age as your dad.) As others have suggested, look at some of the self-drive options with tour companies to see their itineraries for ideas.
PS--To really make thing easier, look at the list of geographic terms in the Rick Strives book in order to understand that place names in Icelandic are just a combinations of various geographic terms: Vik=harbor; reyk=steam; Reykjavik=steamy harbor; Jokulsarlon=glacier lagoon, etc.
Let us know what you decide, and how your dad enjoys it.
