Every night at midnight, generate 2 random numbers between -1000 and 1000 (I use random.org)
Travel to the location with those numbers as the X and Z coordinates.
Create a house centered on those coordinates.
You can do anything with whatever time you have left over, like mining for materials.
The first day can be spent getting basic supplies/tools.
If you fail to get to the location and build a house by midnight, throw away your most valuable item (this includes tools. Say bye-bye to your diamond pick!)