Ooh, that sounds exciting! Where to go / what to see is heavily dependent on how you plan to get around, and also what you like to do (clearly you enjoy the cities but do you also like to escape into the countryside as well?). Also, where are you flying into and out of? Almaty or Bishkek? Make sure that you do your research regarding which border crossings are currently open to foreigners - I found Caravanistan was a good source:
https://caravanistan.com/border-crossings/
Kazakhstan and Kyrgyzstan are both quite different from Uzbekistan in that they're mostly lacking the amazing mosques and Silk Road / Timurid treasures - but then again you've probably had your fill of those anyway.
The area around Almaty in southern Kazakhstan is probably the most beautiful and interesting in the country, and not typical of this vast country which is mostly pretty featureless steppes. Almaty itself is a pleasant city, with a nice setting in the foothills of the mighty Tien Shan range. It was noticeably wealthier and more westernised than any other city we saw in Central Asia - that makes it both easier and more comfortable, and also somewhat more expensive and slightly less exotic/interesting. Charyn Canyon looks gorgeous - we had planned to go there but our itinerary got too tight and we had to prioritise other things, but from what I hear and read it's worth a look (and can be conveniently combined with
Kolsai Lakes/Lake Kaindy sunken forest).
Caravanistan seems to show the border crossing between Charyn Kanyon in Kazakhstan and Karakol in Kyrgyzstan to be open these days, which is convenient - it wasn't when we were in that part of the world, which is the main reason we didn't make it to Charyn Canyon. However you would definitely need to do your research around transport options. We had our own vehicle so never had to wrap our head around that. The routes from Almaty to Bishkek or Almaty to the resort towns on the northern shores of Issyk Kul are quite heavily travelled and should have a few options, but the other roads in the region are very lightly trafficked.
In my opinion, what really makes Kyrgyzstan worth visiting is the incredible alpine scenery and the yurt-based nomadic culture, so to see the best of that country you really have to get out of the cities. By far the best thing we did in Kyrgyzstan was to make it up to gorgeous Song Kul lake, 3,000+ metres up into the mountains and surrounded by beautiful alpine grasslands and the Kyrgz people grazing their stock on their summer pastures. I believe there are various places where you can stay in yurt camps etc - we had our own camping gear so did our own thing.
We also enjoyed the north shore of Issyk Kul, though these are basically resort towns, filled with (frequently drunken) Kazahks and Krygz holidaymakers, with all the tackiness and rowdiness that implies. We never made it to Karakol, though I hear that's nice and has some great day hikes. Another highlight of Kygyzstan for us were the cities of Osh and Jalalabad, with their lively markets and very different cultural feel, but they are at the other end of the country so probably not worth going vastly out of your way for. We never made it to Bishkek, and my impression is that we didn't miss a huge amount, though if you love Soviet architecture you'd be in for a treat (check out
swingaling's
excellent recent trip report for a good account of Bishkek).
I would try to find some kind of tour that would get you up to Song Kul and into the mountains - there will probably be options, based out of Bishkek or Almaty. Or of course you could hire your own vehicle if you were comfortable doing that - everywhere I've mentioned is accessible via 2WD, though depending on what you're used to some of the roads are a little challenging.