I have heard a lot that Lord Hanuman is immortal but I want to know where he lives?
Yes Lord Hanuman is still on this planet. Shrimad Bhagvat Puran Canto 5 Chapter 19 mentions that he lives in the Kimpurush Varsha listening to Ramayan being sung by the denizens of the place and himself joining them in the singing:
किंपुरुषे वर्षे भगवन्तमादिपुरुषं लक्ष्मणाग्रजं सीताभिरामं रामं तच्चरणसंनिकर्षाभिरतः परमभागवतो- हनुमान् सह किंपुरुषैः अविरतभक्तिरुपासते ।
आर्ष्टिषेणेन सह गन्दर्वैरनुगीयमानं परमकल्याणीं भर्तृभगवत्कथां समुपशृणोति स्वयं चेदं गायति ॥
S'rî 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 always engaged there in worship of the Supreme Lord Râmacandra, the Original Personality who as the elder brother of Lakshmana is so pleasing to Sîtâ.
Together with Ârshthishena [the leader of Kimpurusha] attentively listening to the stories about his most auspicious master and Lordship being chanted by a company of Gandharvas, he [Hanumân] himself prays thus.
Coming to the location of Kimpurush Varsha, it is stated to be situated north of the Himalayas which could refer to the northern range of the mountains since Mansarovar Lake is also associated with it.
Hanuman is a son of Vayu. According to Valmiki Ramayana he lived in Kishkinda the capitol of the Apes which were called "Kimpurushas" in Srimad Bhagavatam 11.16.29 and are according to Mahabharata 1.66.8 offspring of Pulaha. Therefore Kimpurusha Varsha seems to be identical with Kishkinda which was located in a hole in the Himalayas. It is said that Hanuman would live as long as the story of Rama (the Ramayana) is told (Valmiki Ramayana 7, 50 + 121; Mahabharata 3.291.44 + 48 f.). According to Mahabharata 3.149.7 ff + 38 he has to change his shape in every yuga. According to Indonesian Ramayana The Uttarakanda 64 his existence will end with the end of our Kaliyuga (according to Rigveda 5.87.4b and Mahabharata 3.189.33 this will take place when the constellation Orion - identical with Vishnu - will arrive its upper point of return in the course of the precession which will be the case in short time).