I would highly recommend staying at the Vallas Apartments. My friend, Amy, and I stayed here in August 2016 and had a very pleasant experience.
We were met by the hotel manager, who I believe is Vaggelis Argiros, when our taxi driver dropped us off. He took our luggage to the hotel for us (a 5-minute walk) and refused to take a tip! Very, very nice man. He then checked us in and wrote on a map so that we would know what was around us and how to get there. He was very helpful in answering our questions about how to get to the bus stop (5 minutes away), Perissa Beach, Oia, and Fira. He was also really nice and let us leave our luggage in the check-in room (since our check-in wasn't for another 4 hours).
Vaggelis recommended Mama Thira Restaurant, which is right next door. What do I say about Mama Thira's...For starters, I literally cried when I ate the appetizer platter. Yes, cried. Then I shook the waiter/manager's hand and told him it was the best thing I've ever eaten. My friend and I went back an additional two times in a day and half because the food was just that delicious.
After lunch, we walked a short (under 10-minute) walk down to Fira, which was all hustle and bustle, leaving us very, very happy that we chose to stay in Firostefani instead. From the Fira bus station, we took the bus to Perissa Beach, which took about 50 minutes. (Make sure you get on the Express Bus, which only took 20 minutes!)
When we got back, our luggage was in our room. We got the key and were delighted to see that the room was so pretty and clean, which a stone bathroom which had hot water in the shower (a luxury not afforded to us in our Oia hotel)! It also had a great air conditioner and two different couches/beds in addition to our double bed, where we could each put all of our stuff.
The view was spectacular. We had breakfast with a gorgeous view of the caldera. (The free breakfast is yogurt and bread and coffee I think, so we ordered off the paying menu and got a delicious chocolate crepe and fresh fruit bowl.) We climbed the steps to the roof and took a literal photoshoot there both in the day (near the small pool) and at sunset. My friend and I both agreed the sunset was much more beautiful -- not to mention less crowded! -- here in Firostefani than in Oia at the castle (which is the supposed "best" place to view the sunset).
The staff at Vallas was really kind and helpful. One waiter even gave me a free glass of fresh-squeezed orange juice in a champagne glass for my photoshoot! They also arranged a taxi to pick us up at midnight (a strange time to check out!) to make our 2:30AM flight, and for the driver to take our luggage to the car for us. This was extremely helpful, as we're two very small girls.
I would 100% stay here again. Our two nights cost us €276 total (so approximately $398 total). I felt $200 night was a fair price for a very lovely room, private rootop with a small pool, prime location, neighboring delicious restaurant, friendly staff, and absolutely stunning view!
Room tip: I'd recommend requesting a room on the second floor, for a view of the Caldera!