We loved our stay at Barbarossa Suites. Location was great - out of the touristy traffic of Thira and Oia. Emporio old town is very very quiet and small, which suited us fine. Couple of lush cafes, and then a bit more going on nearer the square. When we fancied something less quaint, we drove a few mins down Perissa beach, where you can get your classic beach/cocktails/gyros/bar fix. The place itself is stunning, beautiful white cave buildings, bougainvillea and cactuses, plus a deep pool to cool off in. We could have stayed for weeks! From other reviews, was imagining all sorts of crazy hill climbs but although the steps up to the house from the street are steep, and roads are uneven, we found it fine, even after a few ouzos.
One thing to note is that we had a small hire car and scratched it on the first day (lol), following Poppi up to the private parking, as the streets are incredibly narrow. Full insurance recommended! We ended up parking a little further down in the public car park most of the time. Also prepare to occasionally see anyone staying in the suites the level below, as they use a different section of the terrace on your level. This was fine for us, as we were all fairly quiet and kept to ourselves, but something to know if you're expecting not to be overlooked.