Heck Neil, I wouldn't worry about getting "unobtainium". Just use sand and pay a little attention to Mr Einstein and you should be able to build a stable structure anywhere you want.
Any shape you want so long as it's round, more or less. Don't expect it to just sit there though
Location may be another problem. Building it amongst the Oort cloud would probably minimize the materials necessary, but the value of real estate in that neighborhood may prohibit the cost effectiveness of the project. Location is everything in the real estate business.
For a million dollars ( I will give you a "quit claim deed" to a million cubic miles of the Oort cloud neighborhood. Heck, I would probably settle for ten bucks if you really want it.
I'm so generous I am always broke