Are there any transparent enclosures or housing options out there for the Stellaris LaunchPad?
I have not seen one.   I intend to make a case using a 3-D printer, but it won't be transparent.

There are no mounting holes because the board is intended to be attached to a larger PCB using the headers.  The larger PCB would have mounting holes.  If you don't have a larger PCB, then you can always use double-sided foam tape.