I think Belle & Sebastian are the one band I can think of that I'd describe as decent twee. But they're not
super twee. Any other tolerable twee I've heard probably comes out of Sweden, Ursula is right.
And it's not that I don't think of uke as a real instrument, I just overwhelmingly associate it with twee. And I admit that that's not entirely fair of me. But it's hard to avoid with all the bad ukelele twee out there! I think the thing is, uke is fairly easy to play/learn. Sure, there are masters of it who can play crazyass technical stuff. But pretty much anyone can learn a few chords and I'm sure we're all aware of how many songs one can play knowing only 3-5 chords. And this seems like what a lot of twee bands do.
Joanna is like the opposite of twee. I think someone who listened to a split second of MEM and heard her high-pitched voice, but didn't listen to lyrics, instrumentation, or chord progressions, might ignorantly refer to her as twee. But here's the differences: Joanna can
really fucking play the shit out of her instrument(s). Despite what haters will say, she can
really fucking sing. I doubt anyone would argue much with you on the intelligence of her lyrics, and if they do, they're obv a moron. PLUS her music is intensely honest and genuine, which is something I find lacking in lot of in twee.