Spend the night in or near the town of Vik. There are small grocery stores and a gas station if you are looking to purchase affordable food to save some money while in Iceland. If you can’t find any accommodations in Vik, try looking near Selejendafoss Waterfall. Although the waterfall is a bit further out and you will have to backtrack, you can find more affordable accommodations out here. You can visit Vik on the third day of your 5 day Iceland itinerary so don’t fret and consider locations all over the south coast for your second night’s accommodation.
How to get to the plane: https://www.findingtheuniverse.com/iceland-plane-crash-dc3-solheimasandur/