As Śrīla Jīva Gosvāmī points out, Lord Balarāma’s journey to Śrī Vṛndāvana is also described in the Hari-vaṁśa (Viṣṇu-parva 46.10):

kasyacid atha kālasya
 smṛtvā gopeṣu sauhṛdam
jagāmaiko vrajaṁ rāmaḥ
 kṛṣṇasyānumate sthitaḥ

“Remembering the deep friendship He once enjoyed with the cowherd folk, Lord Rāma went alone to Vraja, having taken Lord Kṛṣṇa’s permission.” The simple residents of Vṛndāvana were aggrieved that Lord Kṛṣṇa had gone to live elsewhere, so Lord Balarāma went there to console them.

Śrīla Viśvanātha Cakravartī Ṭhākura addresses the question of why Lord Kṛṣṇa, the great ocean of pure love, did not also go to Vraja. In explanation the ācārya provides the following two verses:

preyasīḥ prema-vikhyātāḥ
 pitarāv ati-vatsalau
prema-vaśyaś ca kṛṣṇas tāṁs
 tyaktvā naḥ katham eṣyati

iti matvaiva yādavaḥ
 pratyabadhnan harer gatau
vraja-prema-pravardhi sva-
 līlādhīnatvam īyuṣaḥ

“The Yadus thought, ‘The Lord’s beloved girlfriends are famous for their pure, ecstatic love, and His parents are extremely affectionate toward Him. Lord Kṛṣṇa 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.”