Where is the dining car at on poptropica mystery island?

The Carrot Diner is on 24 Carrot Island. The waitress there is involved in the quest, because she can supply milk to fill the cat's bowl from the old farmhouse.

Also there is the "hair coloring" drink machine. You can mix the various drink colors to create hundreds of shades, then drink it to change your hair color. This is a free coloring feature similar to (but more variable than) the "skin coloring" balloons given out by the balloon man on Early Poptropica.