Suggestion of artists.

So, I need some new music to listen to

Anything close to the genre of these bands/artists:

Kaki King(obviously)
radiohead
Muse
Jeff Buckley
The Cat Empire(especially these)
The Wombats
Cake
Jack Johnson
Jason Mraz

Especially looking for a good Jazz band similar to The Cat Empire.

Well...

Elliott Smith
https://www.youtube.com/watch?v=hHDbCC0Ongs

Michael Hedges
https://www.youtube.com/watch?v=WO5lzjDw87Q

Chris Whitley
https://www.youtube.com/watch?v=n3FROVl5wpI

These three artists are gone... way gone

There's this guy I found on youtube named dustin prinz. He kind of sounds like Jack Johnson.

Cool. I'll definitely look into getting some of their stuff.

But unfortunately, I still haven't found a good Jazz band, so keep the suggestions coming!

You might want to try something like Pandora ( http://www.pandora.com ). Basically, you tell it a band you like, and it selects music for you based on that. As you go along, you can tell it which songs you like and don't like, and it will tailor your listening experience accordingly.

Not sure the band you mentioned is exactly jazz. Jazz influences, probably, but not quite.

If you do like jazz, though...

John Coltrane (anything with McCoy Tyner is awesome)
Pat Metheny (Check out Trio 99>00 or Trio Live: http://en.wikipedia.org/wiki/Trio_%E2%86%92_Live )
Louis Armstrong (considered by many to be one of the fathers of jazz)

As far as modern stuff goes, The Bad Plus is apparently rather highly regarded. I haven't listened to them much myself, but they just released a new all-original album.

I had a listen to the Cat Empire and to me they sound closre to Funk/Ska than to Jazz.

If you want to listen to some Jazzy Funk, try them: https://www.youtube.com/watch?v=nTDaTVRuLug
Or you might look for Calibro 35.

If you want to listen to some modern Jazz/Fusion try checking out Brad Meldhau, Pat Metheny, Mike Stern, Jaco Pastorious and the Weather Report...

If you want to listen to some great classics of Jazz, it's something I'm currently exploring and artists I liked so far are: Thelonious Monk, Miles Davis, John Coltrane, Charles Mingus, Chet Baker, Duke Ellington...

I don't really like Ska that much, so I don't have names to suggest...

If you like bands like Radiohead, Muse, Buckley we have a lot in common... Have you ever listen to the old Coldplay albums (Parachutes and A Rush of Blood to the Head)? They're worth listening to, very different from the following albums, especially Parachutes.
You should try listening to The Cure, The Smiths, The Pixies, Echo and the Bunnymen. Bands like Radiohead and Buckley were highly inspired by them.

Then if you want to listen to some nice Post Rock I suggest you go for Slint, Karate, Sigur Ros...

Let me know if you like any

Wow. thankyou all. this massive list of artists is gonna take a while to sort out
I found some more artists via 'Pandora', and I'll listen to all the others once my internet is un-capped.

uh oh, also King Crimson.
one of the first bands to mix rock and jazz influences back in the sixties. prog rock at its roots (and possibly at its best, too).

SUUNS

Most of the stuff you've already been recommended i'll put a second on!

Some suggestions i'd make:

Porcupine Tree. British band that have been around for quite some time, but have the most versatile style throughout their discography. Early albums sound kind of psychedelic/prog, late 90's are more alt-metal, & their latest is probably somewhere in between Radiohead & muse (with a bit of Tool....which you might also want to give a listen)

Assuming you didn't get to grow up with them, The Smashing Pumpkins. albums Siamese Dream, Melancolie and the infinite sadness & Adore, should be on your 'to be listened' pile at some point.
Sticking with the 90's *sighs nostalgically* I can't recommend Garbage highly enough.
See also Björk, Placebo, Nine Inch Nails, PJ Harvey & Massive Attack.

You've got a lot of different styles on offer, if you like even a handfull of them, most of the artists will lead you to similar artists in their respective genres.

All the best! Let us know what (if anything) ends up grabbing you