We went last week of July, first week of August for 12 or 13 days. It never got completely dark. Camping, you might take sleeping masks (eye cover thingies).
Weather was, well, be ready for cool and rainy. Expect wind. You'll probably get some sun.
We stopped at this grocery store on the way out of Reykjavik:
It's in a mall. This particular store had a wider range of foods than others. Supposedly the most similar to a US supermarket. We did Bonus pretty much for the rest of the trip. We were able to take about 2, maybe 3 days worth of cold food in the soft side cooler for 4 people.
We got a small suv too. Was supposed to be a Hyundai Tuscon 4x4 diesel. Don't remember the model we actually got, but it was a diesel all wheel drive. Did not do the extra insurance. I'd still recommend a rooftop box (32,000 isk). We also paid for extra driver (8,500 ISK) and that was money well spent. TAKE GOOD PICS OF THE WHOLE CAR before you leave the lot!!! They tried to charge us for a gravel ding that I'm sure we didn't do. WRT extra insurance - ash/sand/gravel is a real risk. Windshield chips/cracks and paint dings are definitely possible. If you get really unlucky, you might get caught in high winds and get ash or sand blasted. Luckily, we were on another part of the island when a wind storm hit.
We have a pile of paper from the trip, including a printed version of the itinerary. And we have a gimongus paper map of the whole island. You are welcome to borrow all. L will have an electronic version of the itinerary.
We didn't do a whale/puffin trip but it was def on the to-do list. I think it was non-refundable and very weather dependent. We did the glacier lagoon boat tour, and a private, guided glacier trek. Seems like every activity you do there is $200 a person (besides hiking).
This hike to the Hot River:
and this hot bath:
Both worth going to. The hot bath was kind of slimy - i didn't get in. But very picturesque. And, if you go up the valley another 200m(?) there's a place along the creek where hot water joins cold.
Go places as early as you can manage. Traffic and crowds get worse as the day goes on.