Baylor Scott and White Medical Center located at 300 University Blvd, Round Rock, Tx 78665 512-509-0100. Lift Their Spirits, One Bloom at a Time Hospital stays can be tough—but flowers have a way of making them brighter. Send a bouquet to add cheer, comfort, and a reminder that better days are ahead. The Flower Box will happily deliver your bouquet of flowers to Baylor Scott and White Medical Center.