That's a toughie - a good gyro is a meal in itself.
How about offering mezethes like kalamata olives, feta chunks, marinated cucumber pieces, skorthalia, taramasalata, dolmades, etc? They're really not sides, in the Greek tradition, but would complement the gyro offering and make for a nice-looking table. You can probably buy most of the makings or even get them ready-to-serve in Greektown.
Tiropitakia could be a nice appetizer. They're a lot of work and disappear fast, but always welcome in the Davooda household!