Ram Navami celebrates the birth of Rama, the seventh avatar of Vishnu, on the ninth day (Navami) of the bright half of Chaitra. It closes the nine days of Chaitra Navratri in many homes. Devotees fast or eat simply, read the Ramayana, sing bhajans and visit temples, and many temples hold a midday ceremony to mark the hour of the birth.
Because the tradition places the birth at midday, the date is fixed by the Madhyahna, the middle part of the day. The festival falls on the civil day on which Navami covers the middle of the Madhyahna (if it does so on two days, the second is taken), and the puja is done in the Madhyahna muhurat shown in the table, which is a window around local solar noon. The exact moment of midday in the window is not clock noon: it is the middle of the time between local sunrise and sunset, so it moves with the season, the city and daylight saving.
Why do cities differ? Navami begins and ends at one instant everywhere, but local noon is at a different instant in each city. If the tithi ends a little before noon in one city it is still running at noon in a city further west, so two cities can keep the festival on different days in some years. Even on the same day, the puja windows are at different clock times.
A calm note: this is a day of devotion and steadiness, and the puja can be as simple as a lamp and a reading. If your family or temple keeps a different day, it is right to follow them. The tithi timing behind the date is explained on our method page.