Strategies for mapping an area perimeter with a mobile robot
To successfully accomplish this, you probably want the following:


Localization Sensors - If you are on a smooth surface, wheel odometry should be enough.  The rougher the area that you are operating in, the more sensors you would need.  Other common sensors for localization: Digital Compass, IMU, GPS, Vision Tracking (Fiducial Recognition), Stargazer (Indoors).  You can also use LIDAR sensors data to do localization.
Obstacle Detection - As Kortuk says, probably a LIDAR.  Possibly a Kinect, since that's the new hotness.  A decent LIDAR will probably start around 1000 USD for a Hokuyo, and go up from there.  You can then put this data into a map.


From a software point of view, there are several options, but the one that I've had good luck with is ROS.  It has a lot of the software features such as localization, mapping, LIDAR drivers.

As far as the actual path, just spiraling out from a central point would work, taking into account obstacles and whatnot.