Gangotri sits at roughly 3,100 metres, twenty-five kilometres above Harsil, at the point where the Bhagirathi is considered to become the Ganga. The temple is eighteenth-century, rebuilt more than once, and small - the scale of the place comes from the gorge it stands in, not the building.
Doing it from Harsil
This is the argument for sleeping in Harsil rather than at the Dham itself. Leave early, be at the temple before the buses arrive, and be back in the orchard for lunch. Ask us the night before and breakfast can be ready early, or packed to take.
The season
The temple opens around Akshaya Tritiya, generally late April or early May, and closes on Annakut, the day after Diwali - late October in some years, November in others - when the goddess is taken down to Mukhba for the winter. Outside those dates there is no darshan at Gangotri.
Altitude
You are going from 2,620 m to 3,100 m and back in a morning. That is a modest gain, but it catches people who drove up from Rishikesh the day before. Give yourself a night in Harsil first, drink water, and do not sprint the last stretch of steps.
Going further
Gaumukh, the actual snout of the Gangotri glacier, is an 18 km walk beyond the temple and needs a permit and a very different level of preparation. It is not a day trip from Harsil.