Lord Vedavyasa lives in the Uttara Badari, not in the Dandaka forest. Now, where is this Uttara Badari? This Badari is different from the Badarinath we see today. And this Uttara Badari is mentioned even in the Mahabharata, Vana Parva, when Sage Lomasha takes the Pandavas and Draupadi on a Tirtha Yatra. This Uttara Badari, also known as Urdhva Badari, is invisible to ordinary people.
Only people with great penance power can go to Uttara Badari. And going there requires great control over one’s senses. They should have the competence to go to Uttara Badari. Yudhishthira himself says this to the Pandavas before going to Uttara Badari. At that time, the Pandavas and Draupadi started going to Uttara Badari by climbing the Himalayas.
After climbing the Himalayas and as they went on in the upper regions, they came to Kimpurusha Khanda, where Hanuman was still there along with the sages worshipping the Supreme Lord Rama. Then came Harivarsha, where Prahlada Maharaja was still ruling and worshipping Lord Narasimha. After that came the Nishada Parvata.
[Image of how Lord Vedavyasa looks as per the Shaastras]
And then, after crossing the Nishada Parvata, the Pandavas reached Mount Meru. Mount Meru was of a very weird shape. Ordinarily, mountains are sharp at the peak and flat at the base. But here, it is the opposite. Meru Parvata is sharp at the base and is flat at the peak. So, this Parvata is in the middle of the earth.
And then, surrounding that, come 4 Parvatas in its 4 directions. One is Mandara, which was used during Samudra Manthan. The second is the Gandhamaadana mountain, from where Hanuman took the Sanjeevani Parvat and brought it to Lanka during the Ramayana. The third is the Mountain Vipula, and the fourth is Mount Suparshva.
These 4 mountains are known as Vishtamba Parvatas. These are near Mount Meru. The Shaastras say that the Surya and Chandra do parikrama around Mount Meru. Kailasa is also near Mount Meru. And there Lord Shiva resides. Today, the Kailasa we see is part of Kailasa Parvata, but the real Kailasa, where Lord Shiva lives with Umadevi, is near Mount Meru.
So, the Pandavas went to the Gandhamaadana Parvata, which is located to the east of Meru Parvata. There is the Urdhva Badri. There were large Badari trees, so big and dense that they prevented sunlight from reaching the ground. That kind of dense forest it was. There, the Pandavas saw Lord Vedavyasa sitting along with His disciples, namely Paila, Jaimini, Vaishampaayana, Shukacharya, Romaharshana, etc.
Lord Vedavyasa was sitting there in the Padmasana position. He was radiating with the brilliance of crores of suns. He had 3 jatas on His head. He was holding the Gyaana Mudra in one hand (Gyaana Mudra is like the Ashirvaada Mudra hand posture we have; just bend the index finger such that it touches the thumb, and that is Gyaana Mudra), and in the other hand He was holding the Abhaya Mudra (Ashirvaada Mudra hand).
His body was the color of rain-filled clouds, similar to Krishna. The smile on His face was enough to dispel the doubts of agyaana and to provide the correct knowledge necessary for Moksha. He had a Srivatsa mark on His chest, and His body was covered with sandalwood paste. Sitting under the Badari tree, Lord Vedavyasa was giving upadesha to His disciples.
Even Nara-Narayana reside in the Urdhva Badari. Today, in the Badarinaath Dhaam, we see His vigraha and His presence, but then in the Urdhva Badari, even today, Nara-Narayana and Lord Vedavyasa are present in real, and not in the form of vigrahas. They are saakshaat present over there. But as I said earlier, one without proper tapasya and punya cannot even see that place. (In the Badarinaath Dhaam and the Urdhva Badari, Nara-Narayana have equal presence; just that, in Badarinath Dham we have the vigraha of Lord Narayana in which Lord Narayana is present, whereas in the Urdhva Badari, Saakshaat Narayana is present there in real and not in the form of a vigraha).
[Image of Lord Narayana of Badarinaath Dhaam and Urdhva Badari]
There, in the abode of Lord Vedavyasa, there is nobody who hates each other, nobody who is jealous of each other, and nobody is there who is arrogant and boasting. Everyone living there are great realised souls and are gyaanis. They live with each other with love, unity, and peace. They treat each other very well, and it is the same as Rama Rajya, because Lord Vedavyasa is non-different from the Supreme Lord Vishnu Himself.
So, in conclusion, Lord Vedavyasa lives in the Urdhva Badari and not in Dandakaranya. This Urdhva Badari is not visible to the eyes of ordinary people, and only people or souls with great punya or with the power of their penance can go there. Even SriMadhvacharya has visited Urdhva Badari to meet Lord Vedavyasa 2 times in His life, as stated by Sri Narayana Panditacharya in the Madhva Vijaya Mahakaavya.
Hope this helps!
Jay SriRam!
ShriBaadaraayana Vedavyasa Abhinna ShriNarayana Abhinna ShriKrishnarpanamastu!