Tributes are sort of like Easter Eggs, but there is an important difference. Easter Eggs are intended to be somewhat hard to find, where Tributes are more in-your-face. Easter Eggs are more commonly located in the artwork, while Tributes are in the dialogue or narrative passages. The Tributes in Batman comics are legendary and extensive. For example, consider this map of Gotham, from No Man's Land: Starting from the upper left, we have the (Irv) Novick Tunnel, the (Bill) Finger River, (Frank) Miller Harbor, Port (Neal) Adams, (Vin) Sullivan Island, (Charles) Paris Island, (Chuck) Dixon Docks and (Bob) Brown Bridge. In this particular case the tributes are located in the artwork, but they are hardly hidden and indeed have almost certainly been introduced in earlier stories.
As far as I can tell, the beginning of the Tributes came during the famed Steve Englehart run in Detective Comics during 1977. Englehart's work started with #469, but the first tribute I noticed was in the following issue:
And Finger Alley was not the only tribute in that particular issue:
In Detective #473, Englehart made a tribute to the then-current Batman writer, David V. Reed:
And to a Silver Age Batman writer, John Broome:
In Detective #474, there was a tribute to longtime Superman editor (and Julius Schwartz's buddy) Mort Weisinger:
BTW, I should mention that while I have certainly heard the Englehart-Rogers run praised for many years, I never really appreciated it until I read through the entire 1970s Batman catalog. It is one thing to read The Deadshot Richochet or The Laughing Fish as individual stories, but when reading them in context, this whole run really pops out as significant and highly influential.