We have been to Iceland quite a bit, and two of those trips were in February. February can have rotten weather, so expect some road closures. Due to that, you will really need to be flexible.
Even though you are from NY, driving in Iceland is vastly different. The winds do blow cars off the road, and there can often be black ice. The roads are elevated and no shoulder and no guardrails, so it is a different beast. Yes, they get snow, but nothing like NY. It's the wind/ice that gets you.
We are not tour people, so get wanting to self drive. On our February trips, we only rented cars for the days that it was nice, and we have extensive winter/mountain driving experience. I remember one of those trips, every road in the country was closed, just to give you an idea.
With all that said, you might consider a multi day tour just so you can leave the driving to others and sit back and enjoy. Just a thought:)
If you drive, I would adjust the itinerary a bit. After Reykjavik I would head to Vik, bypassing the Golden Circle for now. Then do Jokulsarlon.. Then head back south and do the Golden Circle. This way, if there is bad weather further up the coast, it allows you to be back closer to KEF at the end so road closures further up would not impact you getting back to KEF for your flight. Honestly though, in February I would skip Jokulsarlon because the boat rides there do not operate in the winter and that is the biggest draw there. Instead, I would allot this time to going up to Snaefellsness (north of Reykjavik). So in essence, do Reykjavik, Vik, GC, Snaefellsness and then back to Reykjavik and/or Blue Lagoon/Reykjanes.
Note that when you go to the Blue Lagoon, the eruption in November 2024 had lava that overtook the main road. There is a little parking lot on the main road before you make the turn for the BL and you can see where the lava stopped on the road. It is very impressive! You really see the magnitude of it. I would not stay at the BL more than one night.
As for hotels and restaurants, yes I have many suggestions;) We almost always book our lodgings in Iceland through booking.com FWIW.
in Reykjavik, these are the places we have stayed and would stay at any of these again (some we have multiple times). Center Hotel Midgardur, Center Hotel Laugavegur, Center Hotel Plaza, The Centrum, 4th Floor Hotel and Hotel Fron. Center Hotels does have apartments now which might be good for you with the girls. Hotel Fron has a penthouse apartment with 2 bedrooms and a good size kitchen/seating area. We loved that as we had 3 of us in that room.
Near Vik, we like the Volcano Hotel. About 45 minutes south of Vik we loved Grund Cabin. We stayed there when we brought our 3 adult kids and it was one of our absolute favorite places in all of our trips.
In the Golden Circle, I would avoid Efstidalur. We stayed there on that same trip and I refuse to go back. The owners were so rude to everyone. I was really shocked, and at breakfast we got up and left as it was so uncomfortable. The next night we stayed at Haholt Cozy House in Laugarvatn which we loved. I really like Blue View Cabins in Reykholt there, but we did that when it was just the two of us so had a tiny cabin. There were larger ones for families, and they have private hot tubs on the deck and sweeping views, so if the aurora is out that is an ideal place to see it.
If you do Snaefellsness, we like both Hotel Egilsen as well as Akkeri Guesthouse. We had two rooms at Akkeri. Both have wonderful breakfasts! There is an excellent restaurant right across the street from Egilsen called Naryrarstofa which I highly recommend!