After leaving Kirkufjara, we went to the farthest spot east on our Icelandic adventure, Reynisfjara. If you seek a black sand beach you can actually walk on (unlike Kirkufjara), then Reynisfjara is your kind of place.
Route 215 branches south off from the Ring Road just before it makes its sharp turn towards Vik. The road ends at a parking lot right at the beach. If you're fortunate, you'll find a spot just off the sand. If you're like most people, you'll be parking on the road. But it's not that a bad thing because 1) you're in Iceland, and it's a beautiful place to get a few hundred extra steps on your Fit Bit, and 2) because maybe you'll see a marvelous work of art like this:
Besides the dark sand, the big attraction here is Hálsanefshellir Cave, a massive cave of black basalt. You'll not have the cave all to yourself unless you arrive early or late, but the area is big enough that it never felt crowded, except when I was trying to get a picture of my daughter sitting on the basalt columns surrounding the cave.