Just got back from a central Asia trip, went back to Uzbekistan and visited Kyrgyzstan, Kazakhstan and Turkmenistan. Of the places mentioned in the OP:

Tashkent: After a second stay at the Lotte, I stick with my comments on Page 1 that the rooms are better at the Miran International Hotel. Everything except the location of the Lotte is terrible, and the aircon barely works.

Khiva: Asia Khiva was as good as you could expect there. Great location as well.

Nukus: Jipek Joly 2. Make sure to stay in the new building (slight further from the Savitsky). The "apartment" rooms were actually quite nice, and brand new.

Ashgabat: Agree re. Oguzkent. I believe it's no longer managed by Sofitel though.

Bukhara: Stayed at Sasha & Sons which was recommended as a more "local flavor" kind of place. I was not a fan. Would have chosen the Asia Bukhara in hindsight.

Samarkand: Grand Samarkand Superior. It's newer and across the street from the Grand Samarkand. The rooms weren't bad. Great aircon.

As far as the other stops in other countries, in case anyone is interested:

Astana: The new Marriot.

Almaty: Ritz-Carlton, the best hotel in central Asia and one of the best Ritz properties I've been to. Surprising and excellent.

Bishkek: Hyatt. Adequate.