Thank you, that information really helps us to help you.
If you are flying in from the US, you do not want to drive very far the day of arrival. So I would not go as far as Stikkisholmur that first night. Go to Borgarnes or just up past that. Then the second night Stikkisholmur. As for what to do along this stretch, here are things we have enjoyed. Hvammsvik Hot springs, Raudfeldsgja Gorge, Vatnshellir Cave, the hike (easy) between Arnastapi and Hellnar and back, Budir (black church), Ytri Tunga which is the seal beach, drive up road 570 to see the glacier, Gurduberg basalt cliffs (and the church just down the road from it), Kurkjufell, Hellissandur for the street art, and then kayaking with Vesture Adventures our of Grundarfjordur. We did the fishing trip, which I was not sure if us ladies would like it or not, but our entire group loved it! He does other kayak trips as well.
I would only do one night in Myvatn. Hike to the top of the crater Hverfjall. On the way, hit GeoSea. Or Forest Lagoon, but I have not been to this one yet, so can't speak from first hand experience. Dettifoss, the east side, is stunning! A rough road, but so worth it and far fewer people than the west side.
I would not stay in Vik for 3 nights. Two at most. Then add in the Westmann Islands for a night. Then add another night in the Golden Circle, somewhere around Laugarvatn/Reykholt.
Instead of Egilsstadir, I would opt for Seydisfjordur. A good hike near Egilsstadir is Hengifoss.
For restaurants, in Stikkisholmur we like Skipper, on the Arnastapi hike there is a nice little cafe at the end of the trail in Hellnar before you turn around to head back, in Myvatn the Vogafjos Farm Resort is excellent for dinner and to stay, At Westmann Islands, Slippurinn is excellent for dinner and we liked Gott for lunch, At the base of Hengifoss is an ice cream truck, in the Golden Circle Mika is not to be missed as well as Fridheimer the tomato place, my husband cannot come to Iceland without having the lamb soup at Gulfoss, lol, Ingolfsskali Viking Restaurant just outside of Selfoss is an absolute must, and then Messinn in both Selfoss as well as Reykjavik is outstanding. Also in Reykjavik, I highly recommend doing the food tour. Other places in Reykjavik that we like are the Seabaron, Forrettabarinn, Sjavargrillid for. the best fish soup and lobster tacos, and the Hlemmur Mathöll food hall where I especially like Skal! there. I know this is a lot, and is just a sampling of the places we have enjoyed, but it should get you started.