What's the best next step after learning all the easier chords? Should I continue filling out my chords (and move on to some harder ones - all of which I learn by playing from Fakes and chordpro), or should I be tring other things?

I don't know much about the higher fretboard (above the 4th fret), and I don't know movable chords. Should I practice scales all over the board, various chords up and down the fret? Are there good songs to learn for this work, or just scale & chord practices?
I know: (and maybe a few more)
A C D E F G
Am Dm Em
A7 B7 C7 D7 E7 G7

I do have a teacher, but she's a music major w/ emphasis on piano - I'm searching for a guitarist, but they're hard to find.

Thanks!