ITINERARY:
Day 1: Arrive in Nukus in afternoon from Turkmenistan border. Overnight in Nukus.
Day 2: Travel to Khiva with car/driver, via Moynaq and 3 desert castles (Ayaz Qala, Tuprac Qala, and Kyzil Qala). Overnight in Khiva.
Day 3: Full day sightseeing in Khiva. Overnight in Khiva.
Day 4: Travel to Bukhara with shared taxi. Bukhara sightseeing in late afternoon. Overnight in Bukhara.
Day 5: Full day sightseeing in Bukhara. Overnight in Bukhara.
Day 6: Travel to Samarkand with Sharq train. Samarkand sightseeing in afternoon. Overnight in Samarkand.
Day 7: Full day sightseeing in Samarkand. Overnight in Samarkand.
Day 8: Travel to Tashkent with Sharq train. Late afternoon sightseeing in Tashkent.
NOTES
Khiva/Nukus private driver recommendation: I will make a separate post to recommend him, but I strongly recommend Ali if you're looking for a driver for Khiva and/or Nukus. Ali is one of the best drivers I've had in my travels all over the world. He picked me up at my hotel in Nukus at 5am and took me to Moynaq and then the 3 desert castles and then to my hotel in Khiva at 9pm. He happily went way above and beyond the call of duty for me, including staying out 3 hours past our "scheduled" arrival time, stopping along the way to buy a watermelon for us to eat, stopping so I could visit a local wedding at 8:30pm even though we were running extremely late, inviting me to hang out with his friends at the Ayaz Qala yurt camp and have free snacks there, etc. Ali is a warm, happy, outgoing person who really loves his job and will do anything to make his guests happy. If you need a private driver for this part of the trip, definitely see if you can book Ali. I booked him thru my Khiva hotel (Meros B&B), and I'm sure you could book him through any hotel. Or you can call him directly at +998907199807.
Hotels: I can happily recommend all 4 hotels I stayed at: Jipek Joli (Nukus), Meros B&B (Khiva), Hotel Hovli Poyon (Bukhara), Jahongir B&B (Samarkand). All 4 hotels are "low to mid range"; none is the absolute cheapest room in town, but I paid about $25-$35 per night for a single room at these places and found all 4 hotels to be a really good value. All were quite clean (by third-world hotel standards), conveniently located to the major sites, and had friendly and helpful staff who could provide you with accurate information. Special mention to Aziz at the Hovli Poyon in Bukhara; he is extremely dedicated and will literally walk you anywhere you want to go if you'd like. Though, WiFi was extremely slow at all of these places (truly a tortoise pace); this may be a Uzbekistan thing though. If you don't mind paying $10-15 more than the cheapest place in town, these 4 hotels will serve you very well.
Trains: I took the "Sharq" train from Bukhara to Samarkand to Tashkent. I used Advantour to purchase my tickets in advance. Their commission is $10-15 per ticket, which I wasn't thrilled to pay but it ensured that my trains would not fill up. Kate at Advantour was extremely responsive and answered lots of other random questions about my trip that I bugged her about. They take major credit cards (4% surcharge), so booking with them is easy.
Shared taxi from Khiva to Bukhara: This was a fairly miserable experience. You need to take a shared taxi from Khiva to Urgench (make sure the driver takes you to the Bukhara taxi stand, not the bazaar -- he'll charge you extra), and then another shared taxi from Urgench to Khiva. Khiva to Urgench is easy and uneventful; about 30 minutes drive and taxis are available at the North gate of the old city. As for Urgench to Bukhara, the road has been fully repaired and it's really a 6 hour drive, but the whole process took 10+ hours with waiting time and stopping time. I was the first person in the shared taxi at Urgench (arrived at about 8am), and it took 2.5 hours for 3 other people to show up and fill the taxi. And then the driver stops randomly on the way to talk to random people, etc. I paid 4k som to Urgench and 65k som to Bukhara. I tried to have my hotel find other people to share a car with to avoid this whole hassle, but nobody else was going that day.
Konye-Urgench border (Turkmenistan) to Nukus: Take a shared taxi from the border to the town of Hojeli (1 or 2k som), and then another shared taxi to Nukus (5k (?); don't remember). The shared taxi at the border will try to gouge you, but be firm.
Money: 3000 som to the USD is easy to find everywhere (Aug/Sept 2014).
Entry fees to sites: Everything is negotiable. You'll rarely have to pay full price if you're good at bargaining. It's possible to sneak into some of the sites, too.
Food: Samarkand had a proper "Western" grocery store right near the Registan, which was really nice. Bukhara and Khiva were filled with markets that seem to sell nothing but junk food (all sorts of cookies and candies imaginable).
Clothing: I had no problems anywhere wearing shorts (knee-length, not short shorts) into the mosques and other religious sites. I carried pants with me just in case, though.
People: Uzbeks were really chill and friendly for the most part. I got quite a lot of attention (and marriage proposals) from the locals in Nukus and Khiva, probably because Bukhara and Samarkand get far more tourists. There are relatively few Americans in Central Asia (a plurality of French, and mostly Europeans in general), so people seemed really surprised to meet an American.
CITIES/SITES
Nukus: I just used Nukus as a base for a trip to Moynaq because I was coming from the Turkmenistan border (Konye-Urgench) which is nearby. I didn't plan on seeing the art museum, and didn't have time. Nukus is a dumpy town, but the bazaar is interesting to the extent that you'll see all the traditionally dressed women and Karalpak faces.
Moynaq: It's basically an expensive trip and a long way to go (2.5 hrs each way from Nukus) to see a few rusty ships fakely displayed on a bed of sand. Nevertheless, I thought it was a cool thing to see and I was glad I went. I also think it would have been unnecessary to go to the actual water line of the Aral Sea; seeing Moynaq was enough for me.
Khorezm Castles (Ayaz Qala, Tuprac Qala, and Kyzil Qala): I very much enjoyed seeing these castles. All three were different from one another, and Ayaz Qala is definitely the highlight with the big and little castles one above another. Some people spend more time visiting 5 or 10 of the desert castles, but I really think that visiting these 3 is enough and it would be overkill to see a bunch more of them.
Khiva, Bukhara and Samarkand: Samarkand was my favorite of the three -- particularly because the scale of the Registan and the tilework of the Shah-i-Zinda (avenue of mausoleums) are unmatchable. All three cities are nice in their own way, but finding yourself in mosque-and-medrasa fatigue is inevitable. One full day is plenty of time to see everything in Khiva, and 1 full day (or 1.5 days) is sufficient to see all of the major sites in Bukhara and Samarkand. Khiva seemed rather touristy because all the sites are so close together, but everyone disappeared in the afternoon and I had all the sites to myself. I was very disappointed that most of the sites in all 3 cities are "ruined" by local vendors selling their cheap Chinese-made junk (t-shirts, magnets, etc.) inside the sites themselves. It totally takes away from the experience and the beauty of the sites; the authorities should keep the vendors out.
Tashkent: I only had a 2-3 hours to see the city, and did an express visit to the Chorsu Bazaar (really big, but it's just a typical bazaar), the Hast Imam mausoleum complex (pretty architecture, but it doesn't compare to the other cities), and the Amir Timur and the Independence Squares (not particularly compelling). It's not the most interesting city ever.