I've been paying more attention to restaurants posting a "Kids Eat Free Day". Here are a few I've been able to confirm so far in Salem. Note that an adult entree (and sometimes drink) will need to be purchased to get these deals.
Sunday - IHOP*
Monday - IHOP*, Cinebarre
Tuesday - IHOP*, Roadhouse Grill
Wednesday - IHOP*
Thursday - IHOP*, Shari's
Friday - IHOP*
Saturday - IHOP*
*Kids eat free every day from 4-10pm. Kids have to order off the kids menu
Kids Eat Cheap
Here is a list of restaurants that almost made the list above. I'm not sure why they wouldn't just offer a kids eat free day instead. I think it's much catchier than saying $0.99 or $1 kids meal, but oh well.
Ram Border Cafe
Kids eat for $1 on Sundays with adult entree purchase (excludes kid steak and kid shrimp).
Guadalajara Grill Inc
Kids eat for $0.99 on Sundays with adult entree purchase (must order off the kids menu).
Kids eat for $0.99 on Tuesdays with adult entree purchase (must order off the kids menu).