According to Lonely Planet, the street address is Zarqaynar 114 and telephone is 160 03 02. I was there a couple of weeks ago. I asked the taxi to take me to Khast Imom. Once you get to the Khast Imom complex, the big mosque at the front nearest to the main road has a sign on it saying "Hazrati Imom - Jome Masjidi." Facing the mosque, with your back to the main road, head down the left side of the mosque. You will come to a couple of buildings after 100m or so. The smaller one on the right is the Moyie Mubarek Library Museum with the qur'an. It has a metal detector outside (although you don't need to go through it). You'll need to take off your shoes to enter, and no photos are allowed inside. The qur'an is in a big display case in the center. Check out other exhibits in side rooms.
The library is on the edge of a large courtyard, and across the courtyard is a medressa which now has souvenir shops. The Imam Ismail al-Bukhari Islamic Institute is to the east of the courtyard across a grass area, and the Abu Bakr Kaffal Shoshi mausoleum to the northeast of the courtyard, also across the grass area.
My opinion: don't torture yourself walking from Chorsu, as it's about 1.5 km, it'll be hot, you may get lost, and taxis are super cheap. You could probably pay 2,000 som from Chorsu to Khast Imom (or 3-4,000 if the driver tries to charge you tourist prices and you can't be bothered haggling over such a small amount of money).