Where in my area should I build my fort

Depending on your location, you have a number of approaches to where your fort can be and how you build it. Dwarf Fortress gives you quite a bit of free reign in this regard especially with the addition of z-axis, but it's important to remember that your dwarves have needs. If you expect to have a long-lived fortress, it is wise to plan ahead.

Where to build

There are some restrictions to what you can build where. It's usually obvious. You can't build on trees or boulders, usually. You can't build on rivers and streams, except you can build on a brook. Make sure you have room to build where you want.

With that said, building your fortress how you want is almost limitless. Feel free to experiment and combine the suggestions here.

Hills

Building a fortress into a hill is probably the simplest way to get your fortress started.

If your area has any slopes or hills at all, you can mine straight into it. It doesn't have to be a tall, flat cliff; You can build into a low slope just fine. A low slope that goes up one level isn't quite as useful as a cliff that goes 3 or more levels up, but it's good enough. Try to avoid digging into a small hill though, as you may want some room to build on the first level.

By digging into a hill, your fortress' front gate is generally easier to defend. An area surrounded in cliffs can make navigation for your enemy (and you) time-consuming, but building into a wall forces your enemy to come at you head-on in one direction. In addition, you can take advantage of the natural landscape to "funnel" enemies together, or carve your own funnel-like entrance, making them easier to hit with siege engines and marksdwarfs in safer locations. Also, this works well with an entrance full of traps.

Flatlands

Building a fortress on flat land is an interesting but slightly more complicated approach.

To start, designate your dwarf to build downward stairs on the surface. Go down one level and designate upward stairs where the downward ones are. Keep doing this until you hit stone. Then mine out your fortress.

While this kind of fortress works, it takes more work to properly defend the entrance. As it is, any enemies can come at you from any direction. Without building some inside defences, you may become victim to a siege early on (once sieges work, anyway).

Alternatively, you can build walls around your entrance, along with a ceiling if you want. Make sure you leave a front door open for your dwarves, or better, build a funnel with lots of traps in it. No enemy will bother breaking down a wall if there's a clear way in. They won't know it's full of stonefall traps.

Building a wall around your entrance opens up a whole new level of creativity. Feel free to make a small tower or keep, or a large castle with catapults on each level, or a stepped pyramid that reaches high into the sky, ect.

Houses, Keeps, and Castles

Instead of mining into the ground, you can make your settlement more human-like. By taking wood and stone, you can build walls and floors that resemble houses, warehouses, castles, towers, and so on. As long as it has four walls and a floor above it, you can make a room out of it. This works well on flat lands, but you can do this pretty much anywhere.

Annoying Obstacles

Be on the lookout for these features in your area. They are probably the most annoying features to deal with when making your fortress. They can be avoided just by paying attention to your biome, usually.

Lakes

These things are just about everywhere, except in scorching or freezing climates. They are not a threat really, just annoying. A lake may hinder your design if you build too close to them. As far as mining is concerned, they go down two levels, so make sure you're mining deeper than that. Same goes for rivers and brooks and the like.

Aquifers

An aquifer will haunt you, anger you, and make wise cracks about your mama. See its description on how to deal with or avoid them.

Creatures

Don't build on an area that might have dangerous creatures. The worst kinds are elephants, carp, and giant eagles. Don't even think about building in haunted or sininster areas and the like, unless you think you're up for the challenge. Look up your biome, then compare them against the creatures list to see what you might be up against.