[bizerl (OP)]

Is a stable orbit acheivable at any distance, or is there some fundamental reason why something really fast couldn't orbit at, say 100m of the surface of the Earth (other than the obvious buildings and terrain limitations)?

[RD]

Q. Is there a minimum orbital radius? 

A. Depends how solid the satellite is ... https://en.wikipedia.org/wiki/Roche_limit

Even if the satellite was rigid,  when it came in contact with Earth's atmosphere it would slow down and the orbit would decay. 

[evan_au]

Assuming the satellite is made out of metal (so it is not subject to the Roche limit), and there is no atmosphere (eg the moon), the only limit on altitude is the accuracy of the orbit insertion, and the height of the mountains.

The twin GRAIL spacecraft mapped the Moon's gravitational field from the very low altitude of 50km. This height was chosen because it let them communicate results back to Mission Control on Earth on a regular schedule. Apart from this communications requirement, they could have orbited lower.

http://moon.mit.edu/design.html