Lord Shiva is said to live on Mount Kailash which is said to be in Tibet.
People claim to have sighted Ashwatthama in northern India.
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There are many gods and immortals said to be living currently on Earth.
An inexhaustible list maybe as follows.
As discussed in Skandamahāpurāṇa 2.1.3, in this answer
Varaha (Vishnu's manifestation) lives on the western bank of the Svāmipuṣkariṇī lake near Tirupati Kshetra.
As discussed here
Lord Paraśurāma still lives as an intelligent brāhmaṇa in the mountainous country known as Mahendra.
As discussed in this Answer
Srî S'uka said: 'In the land of Kimpurusha the supreme and greatest devotee Hanumân delighting in service at His feet is together with the people...
As discussed in this answer
Both Hanumana and Vibhishana are supposed to live on earth till the history of Lord Rama remains current:
Chapter 121, Uttarakanda, Valmiki Ramayana
Rama then said to Vibhishana the king of Rakshasas: As long as people shall breathe, O Vibhishana, O highly powerful lord of Rakshasas, thou shalt preserve thy body in Lanka.
As long as the moon, the sun and the earth shall exist and as long as my story shall remain current, thy kingdom shall be in existence.
Having thus addressed the king of Rakshasas always obeying Raghava s command, Kakuthstha said to Hanuman "It is settled that thou shalt live forever, do thou, now observe thy promise. As long as my history shall run current in this world do thou at my command live happily." Being thus addressed by the high souled Raghava Hanuman attained to great delight and said: As long as the sacred theme shall pass current in this world I shall live here carrying out thy commands.
Vishnu Purana: Book IV: Chapter IV:
Maru, who through the power of devotion (Yoga) is still living in the village called Kalápa, and in a future age will be the restorer of the Kshatriya race in the solar dynasty
On a side note, Asura king Mahabali lives in the Sutala-loka, as discussed in this answer
God Varaha, Parshurama, Hanuman, Vibhishana, King Maru and Devapi, and many others are are said to live presently on Earth in the Kaliyuga.
Note that this list is not an exhaustive list.
Bhagwan is said to be omnipresent, and that makes this question not correct, Sri Tyagaraja swamigal said that Koorma is still living in the beach and the sound of beach is the sound of him breathing, Krishna does live in the hearts of his devotees and this was the reason Kulasekara Alwar used to worship devotees rather than Bhagwan. So all of this shows God is still with us today!. Also people say they have spotted Hanuman chanting Ram in the himalayas. Markandeya Maharishi who has blessings of Lord Shiva has no death so he too is with us right now
Even Vyasa Maharishi, Aswathama, Bhalichakravathy, Hanuman, Bhagwan Parshuram, Vibhisa, Kripacharya are all immortals with respect to Padma Puran