śrī-śuka uvāca
balabhadraḥ kuru-śreṣṭha
bhagavān ratham āsthitaḥ
suhṛd-didṛkṣur utkaṇṭhaḥ
prayayau nanda-gokulam
sri-sukah uvaca -- Sukadeva Gosvami said; balabhadrah -- Lord Balarama; kuru-sreshtha -- O best of the Kurus (King Parikshit); bhagavan -- the Supreme Lord; ratham -- on His chariot; asthitah -- mounted; suhrit -- His well-wishing friends; didrikshuh -- wishing to see; utkanthah -- eager; prayayau -- traveled; nanda-gokulam -- to the cowherd village of Nanda Maharaja.
As Srila Jiva Gosvami points out, Lord Balarama's journey to Sri Vrindavana is also described in the Hari-vamsa (Vishnu-parva 46.10):
kasyacid atha kalasya
smritva gopeshu sauhridam
jagamaiko vrajam ramah
krishnasyanumate sthitah
"Remembering the deep friendship He once enjoyed with the cowherd folk, Lord Rama went alone to Vraja, having taken Lord Krishna's permission." The simple residents of Vrindavana were aggrieved that Lord Krishna had gone to live elsewhere, so Lord Balarama went there to console them.
Srila Visvanatha Cakravarti Thakura addresses the question of why Lord Krishna, the great ocean of pure love, did not also go to Vraja. In explanation the acarya provides the following two verses:
preyasih prema-vikhyatah
pitarav ati-vatsalau
prema-vasyas ca krishnas tams
tyaktva nah katham eshyati
iti matvaiva yadavah
pratyabadhnan harer gatau
vraja-prema-pravardhi sva-
liladhinatvam iyushah
"The Yadus thought, 'The Lord's beloved girlfriends are famous for their pure, ecstatic love, and His parents are extremely affectionate toward Him. Lord Krishna is controlled by pure love, so if He goes to see them, how will He be able to leave them and come back to us?' With this in mind, the Yadus prevented Lord Hari from going, knowing that He becomes subservient to the pastimes in which He reciprocates the ever-increasing love of the inhabitants of Vraja."