There are various types of places where Buddha stayed. The most important kind are those monasteries which were given for his (or the Sangha's) use. Also, sometimes he was invited to stay in someone's garden or house, or he just stayed in the wilderness (a forest without owner). All these places are located in the Gangetic Plain (located in Northern India and Southern Nepal).
Monasteries Owned by the Sangha. Originally offered to Buddha and/or the Sangha.
Savatthi: Jetavana. The following huts were used by Buddha: Gandhakuti, Kosambakuti Pubbarama. Migaramatupasada Rajakarama
Rajagaha: Veluvana: Kalandakanivapa Jivakambavana Gijjhakata
Kosambi: Kukkutarama Ghositarama Pavarika-ambavana Badarikarama
Vesali: Kutagarasala Ambavana
Kapilavatthu: Nigrodharama
Saketa: Kalakarama
Gardens
Buddha used to stay there as a guest in someone's garden or forest
Kosambi: Udakavana
Nalanda: Pavarika's mango grove
Thullakotthika: Koravya's Migacira Park
Kammassadhamma: The fire-hut of a brahmin of the Bharadvaja-clan.
A wilderness area
These places had no owner, and generally nobody lived there.
Bodhgaya: - Mahabodhi tree and surroundings
Benares: - Isipatana (Sarnath)
Gaya:Mentioned in "Suciloma Sutta" in the Sutta Nipata - Gayasisa hill
Savatthi: - Andhavana
Kosambi: - Simsapavana
Campa: - Grove of Champaka-trees
Parileyyaka: - Rakkhitavanasanda: Bhaddasala tree
Saketa: - Anjanavana
Vesali: - Beluvagama village
Mathura: - Gundavana
And many other places...
Status not (yet) sure
Mithila: Makhadeva ambavana
Alavi:Mentioned in "Alavaka Sutta" in the Sutta Nipata Aggalava Cetiya (shrine)
Pataligama: Kukkutarama
Bhaddiya: Jatiyavana
Kajangala: Veluvana Mukheluvana
Kimbila: Veluvana
Rajagaha (Other places): Sítavana Pipphaliguha (Pipphali cave) Udumbarikáráma Moranivápa: Paribbájakáráma Tapodarama Vediyagiri: Indasálaguhá Sattapanniguhá Latthivana Maddakucchi Supatitthacetiya Pásánakacetiya Sappasondikapabbhára the pond Sumágadhá.
Vesali: Pátikáráma Válikárám Udena cetiya Gotamaka cetiya Sattambaka cetiya Bahuputta cetiya Sárandada cetiya Kapinayha cetiya
See also
Buddhist pilgrimage sites Parikrama Yatra
Sources and References Sutras in the Buddhist Canon often begin with a statement of location, as in this arbitrary example from the "Parābhava Sutta" from the Sutta Nipata:For more detailed references, try checking the Wikipedia article (if it exists) for the specific location.