Johnny first steps into the Boston Observer's office because, "Above one tiny shop he saw a sign that attracted him. It was a little man in bright blue coat and red breeches, solemnly gazing at Salt Lane through a spyglass" (3.1.16). As the rebellion builds, Johnny will essentially become a spy, or at least he will engage in a lot of information-gathering opportunities.
When Mr. Lyte threatens him with a voyage to Guadalupe, Johnny seeks the Boston Observer's office as a place of safety: "Salt Lane at last, and the little man observing Boston so genially through his spyglass" (5.1.38). The newspaper becomes Johnny's home; this welcoming figure welcomes him.
We think it's interesting that the figure is observing Boston so kindly through his spyglass and that a figure who is meant to be a spy appears to be so welcoming. Spying and openness aren't two things we usually put together, but here it works because, like the man on the sign, the Boston Observer wants what's best for Boston, but is willing to put Boston through some scrutiny to find out what that is.