Non-profit museums, colleges, and schools can request space shuttle tiles and other excess property from the NASA program at this website: GSAXcess.
There is a multi-stepped process and frankly, I’m not sure exactly how to do it. But clearly you start by registering at the site; something I can’t do because I’m not affliated with a school or museum. One side says the deadline for “pre-screening” is July 27th, while the middle column says the shuttle tile requests are closed until September because of summer break.
Prescreening Period 7: Start Date – 06/15/2011; Internal prescreening ends – 07/06/2011; External prescreening ends – 07/27/2011 (Includes Shuttle, Hubble, Apollo, and International Space Station artifacts) New!
Either way, you can ask for anything on their list (apparently you go through a list and put things in a shopping cart like many online sites) and you pay only SHIPPING.
For example, shuttle tiles, probably the most obvious item in my opinion, will show a cost of $1000, but that is their book value of it. Any school requesting one would pay only around $24 for shipping.
The right hand side of the above linked website shows two ways to request an artifact. If you are requesting through the Federal Surplus Personal Property Donation Program, you don’t enter your NCES number but follow one procedure, and if you’re requesting directly from NASA you use another procedure. Perhaps the first one puts the shipping costs on the taxpayer dime so there are more hoops to jump through.
Shuttle tiles aren’t the only objects. A quick slideshow shows a spacesuit glove, a laptop without a harddrive, all the way up to an orbiter payload bay mockup. Can’t imagine the shipping on THAT one.