Krishna Paramatma stayed for 11 years in Gokul as per available information. Let us review the reason:
Whenever incarnation takes place, several pending wishes, boons, curses ( by Rishis and good people ) will also be settled by Vishnu.
Accordingly he stays in different places for different periods according to his plan.
It is said that after Brahma performed penance for 6,000 ( his divine ) years (some interpretations suggest 60,000 years), he caught a glimpse of the toenail of Goddess Radha. When he distressedly appealed to Vishnu, he was told, "Radha will manifest in Vrindavan during the Krishna avatar; you may behold her then and attain salvation."
Many of us are aware of the love between Radha and Krishna and know that Radha was Krishna's beloved. Goddess Radha manifested in Gokulam as the daughter of Vrishabhanu.
There is a beautiful story behind this.
Radha once harbored a desire. It is often said that the pangs of separation (viraham) are sweet; however, she had never experienced such separation because she and Krishna were essentially one. Philosophers believe she was born as a Gopika (cowherd maiden) specifically to understand the nature of this separation.
Mantras have presiding deities. When Vedic mantras were chanted in penance dedicated to Vishnu, He asked what was desired. When they asked, "We have been singing Your praises for ages; when will we merge into You, and when will You bestow Your grace upon us?" He told them to be born as Gopikas during His incarnation as Krishna. The Gopikas are also known as the Upanishad-kantas (the embodiment of the Upanishads).
Radha Devi also manifested as a Gopika, and through the divine Rasa Leela, Krishna granted liberation to all the Gopikas.
For some commitments, Krishna stayed in Gokulam for 8 years.
Subhamastu