For a boutique hotel in Tashkent I would recommend the Hotel Elite, the address is: Usuf Khos Khodjib Street 75/10, Tashkent 700063. I spent 2 nights there and was really pleased with the standard/quality of my room and efficient service of the staff. The breakfasts were also excellent, lots of choice was available. The hotel is in a convenient and leafy area near the Park Bobur and not far from the airport.
I didn't stay in any other "boutique" hotels during my trip around Uzbekistan but can recommend the following if you are willing to consider non-boutique hotels:
Emir Hotel (Samarkand). It's address is: 142, Ok Saroy Street, Samarkand. It's a small private family-run hotel, situated in the ancient Makhalla, close to Gur Emir, the world-famous family mausoleum of the Timurids. Nearby are the Rukhabad Mausoleum and Ak-Saray Palace and the other historical sites. The rooms are not large, but comfortable. The family who run the hotel invited me to eat with them in the evenings at no extra cost.
Hotel Islamek (Khiva): It's address is: 60, Toshpulatov Street, Khiva. It's located in the center of the the old city, right near the ancient wall and very close to historical architectural monuments like the caravansaray, Tash-Hauli Palce, Amir Tora Madrassah, Tranb, and the bustling market. The owner helps to arrange excursions, particularly to the Aral Sea and his son speaks excellent English. They allowed me to sit on the roof top to enjoy the views and take photos. Very friendly place and good quality rooms. The only part that I wasn't impressed with was the breakfast, the only edible part of the breakfast for me was the bread :-/ Otherwise though it was a good choice of hotel.