Gangotri is the jumping off point for the trek to Gaumukh (the source of the Ganges) and the beautiful meadow of Tapovan which sits above it. You will need to get a permit for this trek in advance from the Forest Department office in Uttarkashi. There is a quota system so you may have to wait a few days to make the trek if its busy. There is another very good trek from Gangotri to the lake of Kedar Tal. A beautiful lake surrounded by a bowl of white mountains adjacent to a glacier. Fortunately you don't need a permit for this trek so if you have time to kill why you wait to do the Gaumukh trek you can trek to Kedar Tal in the meantime. The trail starts on the other side of the river from the main town and temple of Gangotri and climbs steeply following the the tributary that joins the Ganges at Gangotri. Its a 46 km round trip to the lake. For the fit and acclimatized its possible to do in a very long day trip but the route is steep and it would be much more comfortable to do in 2 days, but you will need a tent or some sort of shelter for this as there is nothing en route.