You didn't say what type of food you want, but in Indio you are probably talking Mexican. We really like Pueblo Viejo Grill on 111 close to Monroe. Warning it can get very crowded especially after 6:30 and it is now a huge place. Full bar with good margaritas.
An inexpensive place also on Highway 111 is Ciro's. The pizza is probably their best dish and the place is also very popular with locals.
We like to have breakfast at Macario's on Indio Blvd. The chilaquiles will make eating the rest of the day unneccesary. We also like El Campanario off of Indio Blvd. for mariscos.
Lastly there is a tiny, inexpensive ,popular, and excellent Mexican place right alongside the train tracks on Indio Blvd. that Indio locals flock to. It is El Mexacali. Don't let the outside of the place fool you. It is clean and comfortable inside with extremely efficient and friendly service. Don't worry if your Spanish isn't good they all speak English. One of the cooks who seems to run the kitchen is a perfect example of a Mexican Grandmother. My wife and I love the place and the passing freight trains will keep you alert.