The main place I saw to grab a bite to eat in Rodeo was the Rodeo Grocery and Cafe. It is located in an interesting looking little adobe and wood building housing a grocery/general store with a small seating area for the cafe on the right. Decor was pretty normal for a cafe; but they also had a nice mural depicting the route of the old US Highway 80 (of which Arizona Highway 80 and New Mexico Highway 80 were a part). There were red, white and blue flowers on each table along with small US Flags. Prominently displayed at the table reserved for the workers was an 8X10 photo of a cute young female soldier in dress uniform. When I inquired about who the photo was of I was told by the cook "That's my granddaughter". This is the kind of place with home cooking, attentive service, and a waitress who calls everyone "honey". I had a large Pork BBQ Sandwich that was very good, Homemade Cole slaw (which needed more sauce) and a Sprite for $8. Open 8AM to 3PM. Serves breakfast and lunch.
Favorite Dish: The BBQ Pork was great.
The Rodeo Tavern open at 4PM Wednesday through Saturday. I was there a little before that so I did not get to go in. Reportedly the food is excellent. They have a special Shrimp Dinner on Wednesday Nights and Pizza on Thursday Nights.
Dress Code: Casual western attire.
The Chiricahua Gallery is a nice little shop selling a variety of items. It specializes in paintings and pottery; but also sells other crafts, jewelry, candles, jelly, organic foods, etc. Everything has a Southwest flavor to it. The lady running the place was very nice. Prices seemed mostly reasonable. Some paintings were around $100 some were more like $1500.