There's not a lot out there in that price range that isn't just a Casio keyboard.
Just to clarify, you want the keyboard to record external audio? Or are you just talking about it recording what you're playing on the keyboard and playing it back while you improv?
If it's the latter, all you really need is a keyboard workstation.
Look through these and let me know if it's what you had in mind:
Keyboard workstations