Gulnara's has long been Tashkent's budget favourite, though it's lost ground to the new hostels in recent years. There's a friendly-family atmosphere in the lovely courtyard and manager Rovshan is very helpful. The shared bathrooms are clean and extras such as a laundry service, luggage storage, vegetarian dinners, airport pick-up and help obtaining a SIM card make this an understandably popular choice.
Chorsu Bazaar is a convenient 10-minute walk away, but the bazaar is dark and empty at night so women in particular should consider using the better-lit Tinchlik metro station after dark. Visa cards are accepted.