According to NASA's Kennedy Space Center FAQ page, you can get a free autographed picture of an astronaut simply by asking!
Q. How can I obtain an autographed picture of an astronaut?
A. You may write or fax your request to the following address for astronaut autographed pictures:
NASA Johnson Space Center
Houston, TX 77058
Here's an official list of active astronauts with direct links to their social media pages. Who knows, maybe you're about to discover your newest favorite spacefaring human!