Here's the first inspiration:
Most mobile NXT robots move on the ground or something horizontal. So how about making something that moves in the other direction... up! There are several different kinds of robots that move vertically. Some examples include:
"Chimmney-Climbing" robot: this kind of robot uses multiple walls surounding it (like the inside of a box) to move up or down. The old LEGO MINDSTORMS forums even held a contest to make a robot like this. Each robot had to travel up two walls on opposite sides of the robot. Here's a picture of the winning robot (note that it's an RIS robot since the contest was held a while ago):
Notice how this robot pushes against each wall to gain enough friction, and turns its wheels to travel up.
"Fence-Climbing" robot: Another way to move vertically is to climb up a mesh-fence (or a metal grill), by grabbing onto the wires in the fence. If any of you got the Ultimate Builder set from the RIS, you may remember a robot that did this.
"Tree-Climbing" robot: Definitely a bit more advanced, but perhaps someone can even find a way to make a robot climb a tree! You might try making a robot that presses wheels on 2+ sides of the tree and rotates the wheels to climb up.
P.S. One of the Blog readers (basicxman) also made a list of robot ideas which you might find useful, here.