I need something useful to build in minecraft?

Build a wheat farm. Punch grass for seeds. If there isn't any grass, kill skeletons at night for bones. Convert them into bonemeal and use it on grassy dirt. Grass should grow and you can punch them for seeds. Wheat will ensure you have a renewable source of food as well as a way to breed animals with. Wheat for cows and seeds for chickens.

Build a cobblestone generator next. Flowing lava meets flowing water (both of them must not be source blocks) produces cobblestone. With this, you are guaranteed unlimited building materials for fortifcations as well as unlimited stone tools.

In the long run, you can aim towards building a villager breeding farm as zombie villagers which has a chance to be spawned at night can be cured and reverted to normal villagers. With at least 2 villagers cured, you can start a villager farm which you can trade with to find your perfect villager. Through trading, you can obtain a lot of useful items in the game, including diamond tools even on a small island.

People would know what things are possible better if you could provide the seed/map (not sure which kind of island you got there). But just guessing, I would suggest making your own village. You said you didn't have villagers so you could make like a ghost town things. It might not be that useful, though, because you could use the furnaces and all, but you would have wasted materials.

Build a rollercoaster. It is a fun ride but also doubles at fast transportation. Make it stop at all the major places you have like a railway system.