The stories say he was a prince in a small kingdom in northern India/southern Nepal around 500 BCE. Were such kingdoms present in that part of the world at that time period? Are there any contemporary records of the time that would help corroborate the story of the life of the Buddha?
The Buddha was born at the time of the mahajanapadas, or the period of the 16 kingdoms. This was at the end of the Vedic period, and the various vedic tribes of North & Central India had settled into kingdoms. This period is variously reported by the religious texts of Hindus, Buddhists, Jains, and by contemporary Greek & Chinese travellers.
While the kingdom of the Buddha, Kapilavastu, is only really known from Buddhist sources, we have evidence of belief in the Buddha and his teaching from only a few centuries later. The Emperor Ashoka (~250 BCE) erected structures honouring the Buddha at sites associated with his life, some of which still survive. Even by Ashoka's day, these sites were well known, and attracted large number of pilgrims. While this isn't evidence of the historic Buddha, it does demonstrate that a handful of generations after his supposed lifetime his cult was well established.
The Jains were a rival religious group that arose in the same region some time before Buddhism, and notes the Buddha as a historic personality, albeit on the wrong path. Buddhist sources often have Jain monks plotting and scheming to assassinate the Buddha.
As to the political organisation at the time, Hindu, Jain & Buddhist sources largely agree on which kingdoms constitute the mahajanapadas, though there are some differences. The Persian Achaemenid empire conquered one of the mahajanapada kingdoms, Gandhara (Modern day Northern Pakistan - Southern Afghanistan), and incorporated it into their Indian provinces of the Indus. This region later fell to Alexander, and the Greek ambassador Megasthenes (~ 300 BCE) to Ashoka's grandfather provides an outsider's view of the period. Strangely, Megasthenes does not mention the Buddha or Buddhism, though he travelled to the capital city of Pataliputra and should have noticed Buddhist structures and followers. Some historians, like Dihle, suppose that this is evidence that Buddhism was only a minor cult pre-Ashoka, and not worthy of mention. Ashoka himself refers to "Brahmanas, Shramanas, and other sects".