From the closest point it is only 1500 meters from shore (a bit less than a mile). If you are staying at the Garden Island Resort hotel, you can rent a kayak from their Aqua Trek scuba shack. From there it is a 2500 meter paddle (about a mile and a half). The currents in Somosomo Strait can be strong, so ask for advice about the tides and the best time of day for making the trip. If you don't feel up to paddling, you can hop an Aqua Trek motorboat for a small fee and they'll drop you off and pick you up later. I've done both, but find kayaking more satisfying. The kayaks have storage where you can stow your snorkel gear, an underwater camera if you have one, and perhaps a small snack and definitely a bottle of water or two. As always in the tropics - especially when going out on the water - apply plenty of sunscreen.
Along the way, the clear, brilliant blue waters change color with the depths and you can see corals and fish below you from time to time. The above water views are of are lush tropical islands wherever you look. It may not be that far, but to save a lot of extra paddling, line up the right edge of Korolevu with an island in the distance and try to stay on that track, keeping the two points lined up, even if wind and/or current pushes you off. You may find yourself paddling slightly at an angle to where you want to go, but your track across the water will be straighter, and thus shorter, that way.
As you get closer, you will make out two beautiful beaches, side by side, with a narrow lava rock wall between them which ends at the water's edge. At low tide you will be able to dash from one beach to the other between waves. At high tide, you'll need to swim or kayak between them. Sea birds live on Korolevu and are a beautiful sight as they swoop over the waves looking for food and showing off their flying skills. Don't worry about bats - they are harmless and won't be out until nighttime anyway when they fly off looking for insects and fruit.
I recommend the beach on your right, as the snorkeling there is excellent. Waves are usually very small and you can just paddle straight in to the beach without worry. Occasionally you may find a local family on one beach out for a day of fishing who may well be curious to learn where you are from and tell you about their fishing luck. Usually, you will have the beaches all to yourself (especially if you kayak in).
Snorkeling around Korolevu is a joy. Be sure to pull your kayak well up the beach - it's your ticket home! There is a long shelf of sand, which allows one to walk into ocean before donning mask and fins. The coral formations are fascinating and there are brilliantly colored fish everywhere. As you go toward the depths you will come to a place where the bottom "drops out" and the water turns a deep cobalt blue and the fish get larger. (I confess that is where I turn around).
After snorkeling, as you rest on the beach, you can gaze at the panoramic view of Taveuni and pick out settlements and the larger buildings - don't look for anything over two stories. Even with its population of perhaps 14,000 and at this relatively close range, evidence of human presence is scant. One can fantasize of a Robinson Crusoe life. After a bit of a rest, a paddle around the backside is recommended. The depth of the water varies greatly, so the color of the water comes in many shades. The rocks and caves are an interesting sight as well.
Somehow, the return trip always seems longer than the one out, but upon your return you can reward yourself with a nice shower and relive your day's adventure over a tall cool drink.
It would be easy to drive right by Korolevu and barely notice it from shore, but now that you know it is there be sure to add it to your list of things to do on Taveuni.