Bhagwan Shiva abode is said to be in Kailash. But at present he doesn't live there, so where does he live now?
The term "Kailash" would be the most prominent answer by many, yet "Kailash" is a metaphorical term (not fictional), meaning, figurative, but don't get offended yet. Yes, there is a significant and breathtaking mountain in Tibet called Kailash which has its own marvel and significance and is backed by scriptures. Even Vedas concur with the notion of Rudra's dwelling to be the mountains [RV5.41.11, TS4.5.5, VS3.61-63] and that Uma is the daughter of those mountains [KenUpa], hence the title Pārvatī (Parvata Raja Putri). But there is no physical proof of Kailash being a mere physical entity with a geographical point that GPS can take us, why? Then where does Śiva reside?
The very Shaivism and Advitam thesis associate creation to be superficial in nature. Yes, Prakṛti is a marvelous imposition by the eternal Maya of Śakti yet is not permanent. The Permanent aspect is always "Śiva" hence the term "SadaŚiva", So what does that really tell us?
Even Vedas confirm that He is “the resort/lord to all hymns/songs”, He is “the resort/lord of all yajñá/sacrifice”, and “He is bliss” [RV1.43] and that bliss is termed Śiva. This Śiva/Rudra is Viṣvarūpam (cosmic form), Pururūpam/Virūpam/Vahurūpa (multiform/multihued) [RV2.33.10,TS4.5.4,TA10.23.1] but in total contradiction, Rudra is Sūkṣma (सूक्ष्म), which means atomic and subtle [RV 7.46, TS 4.5.9, BUpa 3.9.4, SUpa 4.16]. So how can we fit that Śiva “the bliss” on a single mountain/location? However, Śankara being on Kailash, and various Rśis visiting Kailash, Śankara and Uma dancing on Kailash, and many more events are mentioned in prominent non-sectarian literature, so how is that possible, is that not contradicting?
Yes, it sounds contradicting, but no. Kailash is the destination marking the end of material life, it's a pleasure/bliss state of reality. A reality that is beyond the senses and superficial state of Physicality. This physicality as mentioned above is nothing but Śakti. But as long as we are in the play of this Śakti, we cant witness (Sakṣhi/Darshana) Śiva (bliss/ānanda). But when we reach the state of consciousness, we reach the reality of Kailash where one can witness Śiva and his Śakti seated next to him. Meaning the Veil of Maya is removed and we can now clearly witness the consciousness that is enveloped in Manas/Aham/Buddhi. But does this statement above backed by any scripture other than Sectarian literature?
Well, we already saw how the Vedas describe Rudra as being the indweller of all and the heart of all Devas [RV 7.46, TS 4.5, SUpa 3.7/3.2, Brūpa]. All possibilities and celestial dimensions that come into being is that Rudra [TA 10.24.42]. How when all possibilities arise in Him, how can He be fit on something or dwell in a specific geographic location?
Rudra is the pure, spontaneous self-experience which is the one consciousness that dwells in all substances. It is the seed of all seeds, He is Prana, He is Atman, it is the essence of this world appearance, it is the greatest of actions. It is the cause of all causes and it is the essence in all beings, though in fact it does not cause anything nor is it the concept of being, and therefore cannot be conceived. It is the awareness in all that is sentient, it knows itself as its own object, it is its own supreme object and it is aware of infinite diversity within itself. This infinite consciousness can be compared to the ultimate subatomic particle which yet hides within its heart the greatest of mountains. It encompasses the span of countless epochs, but it does not let go of a moment of time. It is subtler than the tip of a single strand of hair, yet it pervades the entire universe. No one has seen its limits or boundaries. ~Yoga Vaśiṣṭham 6.1.36 Swami Venkateshananda
Rśi Kasyapa said, ‘Rudra exists in the hearts of men. He destroys the bodies themselves in which he dwells as also the bodies of others. Rudra has been said to be like atmospheric visitations and his form is like that of the wind-gods. ~Mahabharata Itihasam, Shanti Parva, Pratap Chandra Roy
All that is (विश्वं) and all beings (भूतं) and all celestials dimensions (भुवनं) and all the wonders (चित्रं) all possibilities and diversities (बहुधा) all that is born/all happening/ all existence (जातं) all that has come into being (जायमानं) is that (यत् =is that Rudra) | Entirety is controlled (सर्वोह्येष) Rudra’s delight (रुद्रस्सन्महो) to him we surrender/salutations (नमो) so it be, said/concluded (अस्तु) ~Taittirīya Āraṇyaka 10.24.42
Yes, Śiva is the indweller of all and all possibilities arise and diminish into him, He is Prana and Atma (BrUpa), then who is this Śankara who is seated on Kailash with Uma, that state of reality (of consciousness) that is beyond physical and how this Veil of Maya be removed? This must be proved by literature that is not cherry-picked by Vedic hymns dedicated to Rudra, nor by Itihasas or other sectarian literature. Well, here is what Yoga Sutras have to say:
“The attainment of Dhyāna Avasta shows that the mind is getting ready for the last stage and the real practice of Yoga. Unless and until this condition is fulfilled the practice of Samādhi cannot be begun and the real secret of Yoga will remain hidden…. When the state of Dhyāna has been well established and the mind can hold the object of meditation without any distractions it is possible to know the object much more intimately than in ordinary thinking. How does the mind interfere with the realization of the very essence of the object? By interposing consciousness of itself between the reality hidden behind the object and the consciousness of the Yogi. It is this self-consciousness or subjectivity, pure and simple, which serves as a veil to keep it separated from the object and to hide the reality he (sadaka) is seeking…. Patanjali calls this disappearance of the mind’s awareness of itself is Svarūpa Sunyam iva. When self-awareness has disappeared, what is left in the mind? Only the object of meditation can remain this is the meaning of the phrase Arthamatra-Nirbhasam… In this Samādhi state there is complete freedom both from distractions and self-awareness and the object alone remains in the field of consciousness… A person that comes out of true Samādhi brings with him the transcendent knowledge, wisdom, peace, and strength of the inner life.” Patanjali Yoga Sutra Vibhuti Pada 1-5 by I.K Taimni.
So Kailash in our mind is in the state of ordinary thinking, and the true Kailash has to be known intimately via Yoga Samādhi. So only those Yogis/Rśis whose Veil that separates the consciousness is removed and the true Svarūpa Śūnyam is witnessed this is called Darshana, where one's own consciousness is its own Witness called Sakṣhi. And these Yogis are the ones who have given us the transcendental knowledge of States beyond the mind’s ordinary thinking. This state is where one can witness that Śiva with his Śakti seated beside him (together they are Śivā). And this state is not external but is the indweller of all and that indweller is Rudra.
So long story short: Currently Śivā resides within. Here is a splendid reference given by @Tezz from Mahabharatam
Sources : Link to Sukshma/Indweller
If we are speaking about Adiyogi Shiva, according to Sadhguru he nay exist here in subtle body or he may be living in another planet, as he probably was a being outside of Earth.
Sadhguru: Moreover, because of the nature of who Shiva was – he was considered yaksha swarupa or not of human origin.
According to Sadhguru, Adiyogi was a being not belonging to Earth, what today people would call an alien. He was a realised yogi who came from another planet around 60,000 years and he taught to Saptarishis around 12,000 years ago. He was the first Yogi on this planet and who introduced spirituality to all humans. Only after Adiyogi Shiva came humans became largely spiritual. This is what Sadhguru says. You can read more about this in his book Adiyogi: The Source of Yoga