Approaching the Unknown was released theatrically (plus on iTunes and Amazon) by Paramount Pictures and Vertical Entertainment, starting June 3, 2016. The film played in the following theaters:

New York: Cinema Village (22 E 12th St, New York, NY 10003) 
New York: AMC 34th Street (312 W 34th St, New York, NY 10001) ~Q&A 
Los Angeles: Laemmle Royal (11523 Santa Monica Blvd, Los Angeles, CA 90025) 
Dallas, TX: AMC Parks @ Arlington (3861 South Cooper St, Arlington, TX 76015) 
Santa Clara, CA: AMC Mercado (3111 Mission College Blvd, Santa Clara, CA 95054) 
Washington, DC: AMC Hoffman (206 Swamp Fox Rd, Alexandria, VA 22314) 
Houston: AMC Gulf Pointe (11801 South Sam Houston Pkwy E, Houston, TX 770890) 
Tempe, AZ: Harkins Valley Art (509 S Mill Ave, Tempe, AZ 85281) 
Miami, FL: AMC Aventura (19501 Biscayne Blvd, Aventura, FL 33180) 
Cleveland, OH: Capitol Theatre (1390 W 65th St, Cleveland, OH 44102) 
Orlando, FL: AMC Disney Springs (1500 Buena Vista Dr, Lake Buena Vista, FL 32830)
If you can't go in person, you can watch it on demand via iTunes or Amazon.

Writer / Director Mark Elijah Rosenberg hosted a Q&A following the screening on Saturday, June 4, 6:10pm at the AMC 34th Street (NYC). Get tickets!