Try Norman's, Papago Plaza, and also deifnitely stop by Cowboy Ciao in Scottsdale for a glass of wine and a nibble at the bar - or dinner. For Mexican, try Richardson's or Los Dos Molinos (kitschy, not incredible food but an experience). Cafe Terra Cotta is also a stop, or if you like try, Malee's on Main. Have fun and ignore the whiners and wailers who insist you can't eat lunch (or dinner) in this town. You can, too.
Staying near Grayhawk- a couple of places close by that you might try.
1- an absolute requirement and don't dare miss it- Greasewood Flat. this place comes complete with a three item menu, a wonderful mix of real and imagined harley riders, leftover real cowboys and a lot of other people. Sit outside on a picnic bench, throw wood scraps in the oil drum fireplace and git yer own beer. Its on Alma School road near Pinnacle Peak.
2.. Just opened- a little place called "Cafe Ted" in the building on the NW corner of Pima/Pinnacle Peak (same building as Michael's). I had a nice duck confit salad, other things looked interesting too. Open til 9 at night with some nice wines by the glass and little hings to eat.
3.. "3 Tomatoes and a Mozzarella", at Miller road and Pinnacle Peak. Owned by some nice people who tell me they opened it because they could not get a good pizza anywhere in north scottsdale. Small menu, pizza, salads and paninni. Nice place.
Enjoy, and don't forget a nice hike into the McDowell Mtns to check out the wildflowers this year.