Hi! Are you looking to save money and shop in grocery stores, or eat in restaurants along the way? If you haven’t seen it, you might want to look at my post about Finding food in Iceland
Grocery stores will become smaller and sparser as you leave the greater Reykjavik area. And their hours will be more limited. Here’s a nice map of grocery stores, though I don’t think it’s complete:
https://guidetoiceland.is/travel-info/shopping-for-groceries-in-iceland
There’s a Kjarval grocery store in Vik that’s a good place to stock up. The opening hours picture in my food post above is actually from that grocery store. Note that they close at 6 or 7 PM every day, and they are closed on Sunday. We got there just after 6 on Saturday evening … the grocery store was closed and wouldn’t open again until Monday.
I don’t remember any restaurants on the South Coast that I would strongly recommend. But let me know what else you are looking for and I can try to help!