Reporting back as promised!
We flew both ways with Uzbekistan airways: excellent legroom, rubbish service and no entertainment whatsoever, we didn't go with kids but it would have been a struggle. But for us, fine (and direct).
We started off in Tashkent, which is an interesting, totally non-touristy city. It doesn't really have much in the way of sights, especially compared to Samarkand etc. I'm glad we went there though, it's an odd mix of spectacular austere architecture and abundant greenery. The atmosphere was oddly solemn compared to everywhere else that we we went, but it's definitely very local. The metro is amazing, very ornate.
Then to Samarkand. The Registan is one of those rare world-famous sights that doesn't disappoint in some way, it's truly amazing, and worth visiting both at day and at night (the ticket lasts all day). Other than that Samarkand is nice smallish city, and not massively touristy.
After that we went on a three day tour/homestay in the Nuratau Mountains, which was the undisputed highlight for me. Beautiful scenery, friendly people, apricot trees, hiking, donkeys, dogs without ears (I don't understand why). All very rough-and-ready, rock hard beds and power blackouts, but the family were lovely and they were excellent cooks. Loved it.
Then on to a desert yurt for the night near a big lake. The scenery on this part of the trip was amazing, huge sweeping desert landscapes, dead straight roads going on for miles, fluffy little clouds. Shepherds with their flocks grazing on the scrubby ground, all very hypnotic.
Finally to Bukhara. I had mixed feelings - it's a beautiful city, chock full of medieval Islamic architecture, but unlike Samarkand it's very touristy, extremely popular with retirees from western Europe on tours - "Silk Road Adventure" in the back pages of the Telegraph type scene. And to a peasant like me, one madrasah looks quite similar to another, so why see seven? The authorities are doing an excellent job of maintaining them, but local life has mostly left the centre and at points I felt a bit like I was in Chessington World of Adventures. That said, if you step 100 yards away from the "old town" you're back in real Uzbekistan; there's a sort a villagey feel even in the centre. I'm glad we didn't go to Khiva, which as I understand it is more of the same. I read somewhere that one should honestly ask themselves just how interested they are in medieval Islamic architecture when creating their Uzbekistan itinerary. I would second that!
People everywhere (perhaps with some exception of Tashkent, which is very urban) were lovely, warm, interested, kind. I would recommend learning a few words of Russian though, that's the usual language for tourism. We barely scraped a 'please' and thank you' and wished we'd bothered. The culture is fascinating - I suppose it's got a central-asian vibe, but since this is my first time in the region it felt completely new. I felt completely safe, the whole time. Not only are people welcoming, but there's also a sense of a heavy police presence, not that as a tourist I was troubled by this. There was absolutely no hassle anywhere, but taxi drivers will quote high fares by local standards; I didn't sweat it though, we're talking £4 rather than £2.
ATMs are everywhere and I accessed by UK account several times without issue - I was worried about this, I think a few years ago this wasn't the case. And everything is very cheap - about 30% of UK prices (and that's in the tourist economy)
Overall, it a strong recommendation from me, for anyone who is thinking about it. It's quite a gentle place so if someone in your party is seeking thrills, I would add in a short side trip from Samarkand to the Fann mountains in Tajikistan, or something.