I feel the same way when I get to HHI. I want something good, kid friendly, can walk to it and can show up in shorts and a tee shirt.
since 1998, my traditional first night meal is at San Miguels Mexican on the Marina. It is across the marina from the resort. 3-5 min walk. Kids like it. the outside seating is great. there is usually a guy playing music and singing on the keyboards. IMHO, the steak fajitas are better than most places, and their cheese enchiladas are good, (made with cheddar and a mild red chili sauce) Their salsa for the chips is really good. I do not like their taco salad. I will be eating here on 5/14 and again on 6/24.
If the weather is bad, then we have guiseppies pizza deliver to the room.
I think all the restaurants along the marina are good, like scotts, etc... but they do tend to be a little more upscale than I feel like getting ready for after a long days drive. I save these places during the week.
Also, you could ride bikes to further off places such as Hilton Head Diner and Guiseppies Pizza, Fudruckers, and Craker Barrel if the last two are still open.