I arrived at 2300 and there is a monopoly of taxis. Frankly, I just wanted to get to the hotel so I hired the official airport taxi (there is a stand before customs, as well as money change facilities). The driver had a little difficulty locating it, but it is actually a couple hundred of meters from a mayor street.
After traveling in China, I was relief to notice that the people at the hotel speak English (thanks Haselbeck). The room is clean and right behind the reception, at street level. Since the windows open, I asked Haselbeck about the crime situation and he laughed, stating that this doesn't happen in Uzbekistan.
Breakfast was very good, with cold meats, eggs, cereal, cookies, cake, tea, coffee and blynis. While having breakfast I spoke to a person from India who was working is Tashkent about how he transports, since the Metro is about 1600 m away. He laughed it and told me to use Yandex Go and order taxis. Great find! They are really inexpensive .