grav ‧ i ‧ tate /ˈɡrævəteɪt, ˈɡrævɪteɪt/ BrE AmE verb [intransitive always + adverb/preposition]
formal to be attracted to something and therefore move towards it or become involved with it
gravitate to/towards
Most visitors to London gravitate to Piccadilly Circus and Leicester Square.