Suitable cities to stay in for one night between KIX and Kanazawa

As another answer I would like to say Kyoto. You can just get on the Haruka express at the airport and get of at Kyoto station 1:15h later(Which is just 5 minutes more than it takes the airport express to get to Umeda).

There are also plenty of sights depending on what time you leave in the morning and there are plently of choices for accomodation.

You would also get a 25-30 minutes shorter trip to Kanazawa since your starting location is a bit closer.

First of all, I assume you will be taking the Thunderbird up to Kanazawa. And if that's the case, your options are as follows:

Osaka ( Shin-Osaka or Osaka ) 30-40 minutes away from KIX

It's a big city, but with lots of variety when it comes to accommodation. Umeda is a major shopping district, Shin-Osaka is outside of downtown and mostly for train transfers. Note that you could also take the Namba Express, which gets you to South Osaka, but you'll have to transfer to get to Kanazawa.

Kyoto ( JR Station ) 70 minutes away

If you go here, you'll want to make sure you get the Haruka Express. It's a great walkable city with a beautiful station, though JR's station is away from the typical places you'd visit as a tourist. There's another station that's better situated and cheaper to get to that we usually take, but JR doesn't run to it.

TSURUGA ( On the Japan Sea ) 90 minutes from Osaka.

On the Japan Sea, almost all thunderbird services stop here. You should be able to find reasonable accommodation here and you'll be a short 90 minutes away from Kanazawa. You could probably be here before 8:30PM if your times line up. Trains leave every 30 minutes from Osaka.

FUKUI ( perhaps pushing it ) 2 hours from Osaka Fukui is the last large city after Kyoto before you get to Kanazawa and the prefectural capital. It's arguable that if you're going to go to Fukui then you might as well travel the last 40 minutes to Kanazawa, but I'm including it for the sake of completeness.