Śrī Rūpa Gosvāmī has taught that living in Vraja is one of the five most powerful items of devotion which will grant love to the lotus feet of the Lord (the others being: Associating with the devotees, worshipping the deity, hearing the Śrīmad Bhāgavata and chanting the Holy Name), because:

anyeṣu puṇya tīrtheṣu
muktir eva mahā-phalam
muktaiḥ prārthyā harer bhaktir
mathurāyāṁ tu labhyate
aho madhupurī dhanyā
vaikuṇṭhācca garīyasī
dinam ekaṁ nivāsena
harau bhaktiḥ prajāyate

(Padma Purāṇa)

 “In other holy places liberation is the great benefit, but Hari-bhakti, which is prayed for even by the liberated souls, is attained in (the district of) Mathurā.
O! Blessed is Mathurā, which is even greater than Vaikuṇṭha! Simply by living there for one day devotion to Hari awakens in the heart!”

The Gosvāmīs have said that living in Vraja is an indispensible item for someone who wants to attain the perfection of love of God: kuryad vāsaṁ vraje sadā.
It has also been advised that those who are unable to live there physically should live there at least mentally, the condition being that one must be aware of the transcendental glories of the dhāma while living there.

One must live there with love, faith, and devotion. If this is not, possible, then one will consider the transcendental dhāma to be a material place and commit offenses there.
In this way one can’t reap the devotional results of living in the dhāma.
Śrīla Kavirāja Gosvāmī has written:

sarvopari śrī gokula vraja-loka dhāma;
śrī goloka śvetadvīpa vṛndāvana nāma
sarva-ga ananta vibhu kṛṣṇa-tanu sama;
uparyadho vyāpī āche – nāhiko niyama
brahmāṇḍe prakāśa tāra kṛṣṇera icchāya;
ekai svarūpa tāra nāhi dui kaya
cintāmaṇi bhūmi, kalpavṛkṣa-maya vana;
carma cakṣe dekhe tāre prapañcera sama
prema netre dekhe tāra svarūpa prakāśa;
gopa gopī saṅge yāhā kṛṣṇera vilāsa

(Caitanya Caritāmṛta, Ādi 5)

 “The topmost abode is Śrī Gokula, or Vraja-dhāma, which is also named Śrī Goloka, Śvetadvīpa and Vṛndāvana.
This abode is endless, all-pervading, and omnipresent and it is just like Kṛṣṇa’s body. It spreads below and above without any rule, but by Kṛṣṇa’s wish, it is manifest in the material world in one form. It has no two forms. The soil is made of Cintā-jewels and the forests are full of desire-trees. The material eyes see it as a material place, but eyes filled with love of God see it in its real form, where Kṛṣṇa plays with the gopas and gopīs.”

Transcendence can never be perceived with material senses, therefore the Lord has mercifully revealed His abode in this world in a form which is visible with the senses.
With this faith, with love and devotion, we must live in the dhāma. If not, then we will certainly commit offenses to this holy place, finding faults in it or seeing it as an inferior place. We will be blessed if we can live in the dhāma with great devotion and full faith that it is a transcendental place, for love for the holy dhāma is the highest pursuit of life.

Śrīla Prabodhānanda Sarasvatīpāda has written:

rādhā muralī manohara caraṇa vilāsena dhanyāyām
vṛndāvana bhuvi manye parama pumartho manāg api praṇayaḥ

(Vṛndāvana Mahimāmṛta 4.65)

 “If I even have a little love for Vṛndāvana, the place which is blessed with the pastimes of Rādhā-Muralī Manohara’s lotus feet, I will consider myself to have reached the highest goal of life.”

Śrīla Sarasvatīpāda, who is filled with love for Śrī Vṛndāvana, shows a wonderful fixation in devotion to and living in Vraja:

śrī rādhā muralīdhara vara dhana
vṛndāvane varaṁ krimikaḥ
bhagavat pārṣada mukhyo’py
anyatrā’haṁ na cotsahe bhavitum
sarva duḥkha daśā ghorā
varaṁ vṛndāvane’stu me
prākṛtā’prākṛtā’śeṣa
vibhūtir api nānyataḥ
paśur ekaḥ khaga ekas
tṛṇam ekaṁ reṇur eko vā
śyāma rasādbhuta vanye
vṛndāraṇye bhavāmyahaṁ dhanyaḥ

(Vṛndāvana Mahimāmṛtam 4.57, 61, 64)

 “I would rather be a worm in Vṛndāvana, the greatest treasure of Śrī Rādhā and Muralī-dhara, than to be a chief associate of the Lord elsewhere. May I get into the worst trouble in Vṛndāvana, but still I don’t pray for having all the material and spiritual opulence of the world elsewhere.
I will feel blessed even if I become an animal, a bird, a blade of grass or even a speck of dust in Vṛndāvana, the wonderful forest which is endowed with Śyāma-rasa!”
(Śrī Rādhākuṇḍa Mahānta Paṇḍita Śrī Ananta Dās Bābājī Mahārāja)