Minecraft wiki entry for The_second_day, associated text: A place to grow wheat:
Even before you have a bucket, you can till the ground next to a river or lake, and plant whatever seeds you have to get an early start. A handful of bread gives you a lot more options.
Later, you'll want a basically flat area at least 12 blocks square, which you can reshape into completely flat. After fencing off a 9×9 square and placing water in the middle (that's what the bucket is for), you can till the square and make a farm to serve you well for most of the game. Watch out for nearby rises that could let monsters jump over your fence.
A place to build a larger house or lair. There are many options here. The most popular options are to build on (more-or-less) flat ground, a roof over a valley, or wall off and occupy a handy cave. You need space for your enchanting table, crafting table, furnace, anvil, and several chests, and of course a secure place for your bed.
Different kinds of trees. Each kind of tree provides logs with a different appearance, and the various trees have different characteristics for farming them (see the "Tree" article for full details). Collect the logs for crafting and building, and the saplings to grow your own.
Keep an eye out for a pond or riverbank site where you can make a fishing spot. Fishing requires time and (for safety) some preparation, but can get you a lot of resources, some of which are difficult to get otherwise. It's also an early way to get good-quality food. If you want some of the treasures you can get from fishing, make sure the bobber is in open water.
One or more cave entrances, to get underground and start collecting iron ore and stone in quantity. If you spent your night in a cave, this might be easy, but for mining, you'll want a cave that heads deeper into the ground.
Any of the various crops. You need to find each of these in the world before you can farm them, but then you'll have effectively unlimited supplies. See their respective pages for how to grow each of them, but several of them can share space in your wheat farm.
Animals, for meat and other resources. Later you can build pens to breed and slaughter them; as with farming crops, you're looking for large, fairly-flat areas that you can fence off and otherwise defend against mobs. You can kill some of the animals now if you need more meat, but leave some of each type to later catch and breed. Once you do start collecting and breeding them, you must go further afield to catch more, as they do not spawn near your farm. (See the Spawn article for more details.) Note that deserts do not spawn any animals except the occasional rabbit.