A two-minute walk down the hill from the house will bring you to Kealakekua Bay. Wonderful to swim in, although it is a rock covered beach and can be dangerous in high surf. This is a dolphin resting area. There is a heiau (sacred temple) that was the site of ancient school for many Kahuna. One mile across the bay is the Captain Cook monument that you can get to by swimming, kayak, or for the adventurous, by trail from the top of Napoopoo Road.
About 4 miles south from the bay is the Place of Refuge Pu'uhonua o Honaunau National Historical Park. This park has a guided tour with many historical structures. There is also a picnic area at the south end of the park where you may see a whale during the winter months. Just before the entrance to the park is '2 steps,' a lava beach, which is well known for it's snorkeling. You may even see a turtle or two.
South of mile marker 102 is Ho'okena Beach Park where there is a sand beach and camping. Many families play in the sun all day. Kayak rentals are available when the concessionaire is there. This is another area where dolphins and whales are frequently seen.
Volcano National Park is about a 2-hour drive from Captain Cook via the southern route. The road is winding but has great stops along the way. Don't forget to stop at Punaluu Bakery as a rest stop and try their lilikoi malasadas. Punaluu is Black Sand Beach and has many turtles resting on the sands. Not the best swimming but some locals do swim there.
It takes about 6 hours to travel the road around the island. Hilo on the eastern side of the island has many waterfalls and is a rainforest. It is lush but often rains. Northeast is Waipio Valley which requires a four-wheel drive vehicle to traverse into. It has a very scenic lookout and well worth the drive. Waimea in the north of the island is an interesting town to visit. Then travel west to Hawi and on to Pololu Valley at the end of the road. This valley has a half hour hiking trail into the valley and is well worth it.
If you have an adventurous spirit you might want to try zip lining. There are three on the island but my favorite is Big Island Eco Adventures in Hawi.
Continuing around the island going southwest, you pass Hapuna Beach Park with a great sand beach but not a lot of shade. Look around the area and you will find a few hidden beaches.
Travel on to Waikoloa where there are many resorts. Try the Hilton for boat rides and tram rides, and captive dolphins that give a fun show. There are many nooks to explore, shopping, and many restaurants in Waikoloa.
Kailua Kona is a great little beach town. Stroll along Alii Drive where you can get a cup of Kona Coffee, sit in a restaurant by the ocean, shop, or just enjoy the waves and the sunsets. Farmers market is open Wednesday thru Sunday but closed on Monday and Tuesday.
Speaking of farmers markets, there are many around the island. Captain Cook has a Sunday market and Keauhou has Saturday and Wednesday markets where you will find local produce and resident artists and their wares. These are a great place to get your gifts for taking home to those unlucky friends and family who didn't get to join you on your wonderful tour of Hawaii.
There are so many interesting places to visit and you can do more exploring on the internet or in a travel guide of the island. Enjoy!