All good suggestions above, I'll add a couple. the area that you are staying in is crossed by the king's trail that goes from Kona to the great Heiau at Kawaihai and there are some amazing petroglyph's fields along that trail. One is at the south end of Puako. Good to avoid lava flow areas in the hot part of the day. Puako is nice in the early morning. good views of Mauna Kea, some times snow capped.
There are some neat old fish ponds just north of Honokahau Hbr. in Kona, its a bit of a walk around the bay just North of the Hbr. Pretty and untrafficted area.
Good sheltered snorkeling with lots of fish in Kahaluu Bch Park, along Alii Dr. between Kailua and Keahou. Popular and developed area, but really good snorkeling.
Kona took a lot of damage from the tsunami. There was a large two story house floating in Kealekakua Bay, Cool Heiau at the Bch there at Napoopoo.
They have been doing a good job cleaning up there, I'm sure it won't effect your visit.
Have fun!!
Richard