Wow I wish I had your problem! I know there are several types of figs Black Mission and Brown Turkey come to mind. As I remember they dry well. Do you know what variety you have? I think you may find figs used more in Middle eastern dishes or Indian. I like eating the dried figs. Good luck on your quest.
Fresh figs with goats cheese and balsamic or with proscuittio are the two dishes that immediately come to mind. That's if you don't want to just eat them!!! (These are the three ways I usually have fresh figs.)
Or how about preserving them in alcohol? Of as oneoffour said, drying them.