Cordoba made a solid bamboo soprano cutaway. I bought one a couple of years ago from Musicians Friend "Stupid Deal of the Day" for $99. I think they retail for $199. I don't play soprano, so gave it to my Grandaughter.
This is actually a good looking uke, too, and exactly in the OP's price range. Not in the market for more ukes right now (this week anyway!), but I'm curious about bamboo as a tonewood (mostly because of its eco-friendliness). What more common wood does it compare to, uke-wise?
I did some searching on line about Paulele ukes. They were carchterized as loud and punchy, with good intonation, but in need of professional set up because the nut is to high. But it's definitely in my price range!