Gravitate to
Definition 1 of 3
Pro Tip 1/3Emotional Pull
Often implies an emotional attraction or connection rather than just physical movement. 
Despite the arguments, she would always gravitate to her family.
Pro Tip 2/3Natural Tendency
Suggests an instinctive action, happening without deep thought or effort. 
Young athletes tend to gravitate to their role models' training methods.
Pro Tip 3/3Subtle Choice
Use it to describe preferences that aren't always immediately obvious. 
At parties, he'd gravitate to the corner to observe rather than mingle.