I visited this WHS in June 2017 and spent 4 days here (1 of them I spent to visit the tentative site Desert Castles of Khorezm).
Again, this is a top WHS even though it is more of a museum-city nowadays. 3000 people are still believed to be living inside the Itchan Kala itself and in fact they have special permits 'to drive home' and park their vehicles inside the city walls! All the sites of the Itchan Kala (inner fortified city) can be visited by buying a cumulative ticket + camera fee from the gate closest to the Unfinished Minaret. It will give you access to 16 different sites but I agree that a local guide for 1 day would be essential to give you more information and context to what you will be visiting - otherwise, it will seem like a nonsensical list of sites most of which now house different kinds of museums. The most interesting was indeed the Khorezm Museum and the Local Photography Museum to see photos of the several buildings and desert castles of Khorezm before the earthquakes and videos of how life was like up to less than 100 years ago!
The only other sites where you'll have to pay again are to climb the 32 metre high Djuma Minaret, the 45 metre high Islam Khadja Minaret, the Kunya Ark viewing platform (photo) and the Pahlavan Mahmoud Complex interior with the Khiva Khans necropolis (worth viewing!).
The best interiors with incredible architecture, art, painted wooden ceilings and decorative blue and white tiles can be seen at the Kunya Ark as well as the Tash Hauli's Harem. The Djuma Mosque's 212 different wooden pillars are a sight to behold and if you have to choose only one minaret to climb, go for this one as it's less claustrophobic and the view of the Islam Khaja Minaret, city walls and Unfinished Minaret are a sight to behold.
In the morning (earlier than 08:30 when the first groups arrive after breakfast), the best thing is to walk on the city walls to see the whole Itchan Kala beneath you and get your bearings if you want to explore more of the inner city and venture past the obvious east-west gate axis.
The most iconic site is most probably the Kalta Minor or Unfinished Minaret with its magnificent turquoise tiles. Based on its proportions, its height would have exceeded 80 metres and be significantly higher than the tallest minaret (62 metres high) in Central Asia in Kunya Urgench, Turkmenistan. The madrasah behind it has been converted into a hotel and restaurant. There is a UNESCO engraved plaque on the western gate just next to it.
All in all, Khiva was one of my favourite WHS in Uzbekistan and definitely a top WHS on the list.