My Grandmother used to live in Mt. Shasta when I was a kid. We used to go to a place called Mike and Tony's. Italian food, great taste, great prices. I ran into somebody from the area a couple years back and asked if it is still around; apparently it is. Sorry, but I don't have directions, I'd stop and ask one of the locals (at a gas station or market) for directions.
If you like breakfast, there is this great little cafe right at the base of Mt. Shasta that serves plate sized buttermilk pancakes, great hash browns, bacon and most importantly, coffee.
I don't recall the name, but it is on a frontage road (of sorts, if I remember correctly it overlooks I-5). Again, you'll have to ask a local.
Sorry for not knowing details, but Shasta is a friendly town, and I'm sure you'll find the places. Besides, food tastes better when you have to 'sniff' it out : )