I've heard Shirdi is considered a pilgrimage site in itself. Is there a story where Baba discouraged someone from traveling to another holy place?

Yes, there is a powerful story in Chapter 4 about this very topic. Das Ganu once desired to travel to Prayag for a holy bath on a special day and went to get Sai Baba's permission. Baba responded, "No need to go so far. This itself is our Prayag; keep firm faith in your mind." In a miraculous demonstration, as Das Ganu bowed to Baba's feet, water representing the sacred Ganga and Yamuna rivers began to drip from Baba's toes. This experience overwhelmed Das Ganu with emotion and solidified the teaching that sincere faith at the Guru's feet is the ultimate pilgrimage.