Hilo International Airport (ITO) is 3 km from downtown and receives direct flights from Honolulu (frequent, about 45 minutes) and from the US mainland. Honolulu connections are reliable and cheap. The airport is small and easy to navigate; rental cars are available at the terminal.
Driving is essential for most of what the Big Island offers. From Hilo, Hawaii Volcanoes National Park is 45 minutes south on Highway 11, Akaka Falls is 20 minutes north on Route 220, and the saddle road to Mauna Kea is about an hour's drive. The Kona coast on the west side is about 1.5 to 2 hours around the south (Highway 11) or the north (Highway 19) of the island. Most rental cars come with unlimited mileage; get one if you plan to do more than walk downtown.