(Sorry, no fotos in this trip report)
Flights to Greenland leave from Reykyavik's "domestic" airport downtown. Took a one-day in-and-out trip on Air Iceland to Kulusuk. No reason to stay on that island for any longer period.
The Faroe Islands are similarly overrated IMHO. The best experience is the dangerous airport approach, for example on Atlantic Airways. I could hear the automatic cockpit warning "Flight into terrain ... flight into terrain ...!" ;-)
Reykjavik has a bit more to offer. Overland island drives are fantastic. Swimming in the Lagoon near the airport is nice. You can easily do the "Golden Ring" in a couple of hours.
These are my hotel observations (on Tripadvisor):
Greenland: Hotel Kulusuk "Complete dissapointment"
This place is a complete joke and to anyone considering a visit to Kulusuk I can only recommend: do the DAY TRIP and don't stay overnight. People at the airport pick up and at the hotel are very unfriendly, service and food levels are among the worst in the world (althought the fish at least is nice and fresh). The hotel is clean, but that is it. There is no interior design, no cozyness, no cuisine, no friendlyness, no activities, no infrastructure whatsoever. It seems that the few residents in Kulusuk live well enough (some Danish transfer system?), so they don't have to bother venturing into tourist activities. Kulusuk is the shortest flight from Iceland and it has a stopover time of 4 hours. I have my doubts that any of the other cities on the island are better. And for out-of-this-world landscapes, one will also find better in Iceland. Period.
Iceland: Hotel Borg, Reykjavik "The closest to being a "Grand Hotel" in Reykjavik”
This is the ONLY hotel in Reykjavik that comes close to being a Grand Hotel with a trace of luxury, beating the Radisson 1919, the 101, the Hilton (in that order IMHO). The location is the best of all hotels, because it is totally central and looks onto a big open square and park with nice outside seating. The lobby and restaurant are certainly of the most expensive and sophisticated design of all Reykjavik's hotels. Some Art Deco furniture. With a price of less than half of the overrated 101, I would definitely recommend the Borg. Overall, the choice of upmarket hotels in Reykjavik is very weak for a European capital city.
Iceland; Blue Lagoon Clinic, Grindavik “Better than the rest, but still rather weak”
If you have an early flight out or a late flight into Keflavik, and if you have a rent-a-car, this hotel may be a recommendation (however there is also hotels directly at the airport). The Blue Lagoon Clinic is one of only two hotels near the Blue Lagoon, and clearly it is better than the Northern Lights Inn, which has no pool/lagoon of its own, which is even farther away and which is even less sophisticated designed than the Blue Lagoon Clinic. Both hotels have equally mediocre service (typical for Northern Europe unfortunately). Both are not really walking distance to the Lagoon, because after the hot water I doubt that one wants to walk several hundred meters in the cold. Breakfast was very weak at the Clinic and starts not before 7.30. What really annoyed me is the closure of the pool between 10 pm and 8am. My flight arrived at midnight and I would have loved to relax in the hot water. It is a shame that with such an asset (the beautiful hot springs in the barren lava surroundinsg) the Icelanders don't provide a better product. If you compare the Blue Lagoon to Thalasso Therapies in France or Spas in Austria/Switzerland or some upmarket Ayurvedic clinics in India, it is really the least sophisticated and least developed in the market.
Faroe Islands: Hotel Streym, Torshavn “A simple bed-and-breakfast”
This is not more than a bed-and-breakfast. The rooms facing the sea are very loud, due to street noise. All rooms are very loud if your neighbour is in. Paper walls. The location is still walking distance to the center, but much farther out than Hotels Hafnia or Torshaven. The correct price in most other places would be around € 30 instead of € 100+. If you look for the best hotel in town, go to the Hotel Torshaven which is totally central, has a restaurant and terrace bar and seems completely newly refurbished in a halfway pleasant scandinavian design style. The other hotels (Hafnia and Föröyar) are run down. Faroer are visually beautiful islands, but if you have a taste for good hotels do not stay overnight. Also, the Faröer's continuing slaughter of whales and dolphins is a reason to stay away.