Hi there:)
As for how to get from KEF to Reykjavik, there are two options that would work well. A taxi of course is door to door, and that has been running about $180 lately. The FlyBus works well too, but you take a big bus to the central bus terminal, then switch to a smaller bus that will take you to the closest bus stop top your hotel. This runs just under $40pp. So a difference of $20. It just depends if you want to save that money, or go for ease of door to door.
I would not rent a car for the time that you are in Reykjavik.
For hotels right in Reykjavik, take a look at any of the Center Hotels. They are equivalent to Holiday Inn Expresses here. The CH Plaza is right smack in the heart of things, so the teens would be able to wander on their own. We are actually staying there again this week when we go.Also look at Hotel Fron, which is also right in the heart of everything and they have a 2 bedroom penthouse. We have stayed in that with our kids. The beds do separate, so the kids do not have to sleep next to their sibling;) I like that room because there is a kitchen, a real dining table, and a sitting area, so you have room to spread out.
The Golden Circle is an easy day trip from Reykjavik. As for Westmann Island, I suggest staying overnight. The reason is the puffins are most likely seen early in the morning or late at night. There is a lot to do on the island as well, and staying overnight would allow you to see most of it. Hike to the top of Eldfell, visit the Eldheimar Museum (a must!!!), do a rib boat safari ride, the beluga whale museum, etc. The kids would love all of this, and not roll their eyes;)
On Snaefellsness, Stykkisholmur is a great place to stay, IME. On one of our trips that we took the 3 adult kids, we stayed at the Akkeri Guesthouse and had two rooms. We loved it! Just next door is Hotel Egilsen which we have stayed at as well. Both are great. You would need two rooms at either one. Or you could look for another place that would have room for all of you, but I can vouch for these two places. I am glad you are allowing several days here. There is SO much to see on the peninsula. We have stayed up there on 3 of our trips and still have not explored it all.
I know we are spoiled with seeing whales here, but when we did the rib boat safari on Westmann, a pod of Orcas came right up to us. The captain saw and shut the engine off and we just sat there. They were SO close!!! And that was not even a whale watching tour!
As for must do tours, besides the rib boat, for Reykjavik and Snaefellsness there isn't any must do, IMO. Now, if you decide otherwise venture up the south coast at all, then yes, the Zodiac boat tour at Jokulsarlon is a must. The teens would love it! What about horseback riding? Or hike to the thermal river on the Reykjanes Peninsula? You don't need a tour for this, but you could drive there and just do it yourself. Or what about a glacier hike? We have done Solheimajokull and loved it. As you can see, the problem, is there is never enough time and just so much to do. Don't worry, just do what you can and know that it's an easy flight to return;)
What about hot springs? I personally love them and we try to hit as many as we can on our trips. In the Golden Circle there is Fontana, Secret and Laugaras (brand new). There is Sky Lagoon in Reykjavik and of course the Blue Lagoon closer to KEF. Just north of Reykjavik on the way to/from Snaefellsness is Hvammsvik which is our personal favorite so far. This week though we are trying Laugaras, which I am excited for:)
I know you are trying to trim your costs, but there is the most amazing restaurant in Stykkisholmur right across the road from the Egilsen called Narfeyrarstofa. I highly recommend splurging on that! It really was not expensive, but the food was excellent. The teens would be perfectly fine there.
