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).
Buddha used to stay there as a guest in someone's garden or forest
These places had no owner, and generally nobody lived there.
Bodhgaya: - Mahabodhi tree and surroundings
Savatthi: - Andhavana
Kosambi: - Simsapavana
Campa: - Grove of Champaka-trees
Parileyyaka: - Rakkhitavanasanda: Bhaddasala tree
Saketa: - Anjanavana
Vesali: - Beluvagama village
Mathura: - Gundavana
And many other places...
Rajagaha (Other places):
For more detailed references, try checking the Wikipedia article (if it exists) for the specific location.
Buddhism (Pali/Sanskrit: बौद्ध धर्म Buddha Dharma) is a religion and philosophy encompassing a variety of traditions, beliefs and practices, largely based on teachings attributed to Siddhartha Gautama, commonly known as the Buddha, "the awakened one".
The following outline is provided as an overview of, and topical guide to, Buddhism.
Topics in Buddhism