Hi- thanks for reading! I do think that Vik is a good home base for the south coast. It’s very close to Reynisfjara and Dyrhólaey. I would stay for 2 nights? But mostly I like having a night where the whole family didn’t have to unpack ad repack!
You could also stay further east if you wanted to, closer to Kirkjubæjarklaustur. That may make more sense if you wanted to head out to Fjallsárlón and Jökulsárlón glacier lagoons.
Unfortunately, sometimes the answer for where to stay on the south coast is “wherever you can find a place.” September should be better than the summer, but your south coast house should be one of the first things you book.
Good luck, and have fun!