To move or be drawn toward something, especially by natural tendency or as if by an invisible force.
Example:
During hot weather, the town's social life gravitated toward the lake.
To gravitate implies a natural, perhaps irresistible, response to a force that works like gravity, drawing things steadily to it as if by their own weight. Thus, moths gravitate to a flame, children gravitate to an ice-cream truck, gawkers gravitate to an accident, and everyone at a party gravitates to the bar.