Sharad Navratri is the great autumn festival of the Goddess, nine nights that begin on Ashwina Shukla Pratipada, the first day of the bright half of the month of Ashwina. The nine days are given to Durga in her different forms; in Gujarat they are the nights of garba and dandiya, in Bengal they lead to Durga Puja, and in much of North India they end with Dussehra. Many people fast or eat simply through the nine days.
The start of Navratri is fixed by the civil day on which Pratipada is in force at sunrise. The festival opens with Ghatasthapana, the installing of the sacred pot, which is done in the first part of the day while Pratipada lasts. When the day is short of time, calendars prefer the Abhijit muhurat around midday. The table shows the window for each city.
Why do cities differ? The Pratipada tithi starts and ends at the same instant worldwide, but sunrise comes at a different clock time in each city. A tithi that ends just before sunrise in one city is still running at sunrise in the next city to the west, which can move the first day of Navratri, and with it every later day, by one. The Ghatasthapana window always differs with the local clock and daylight saving.
A calm note: the nine nights ask for regularity more than perfection. A daily lamp, a short prayer and a simple meal is a full observance. If your family or temple names a different starting day, follow them. Dussehra, on the tenth day, has its own page of dates.