You can ascend the Cathedral spire from 9 to 5:30 in the summer. Cost is 3 Euros, free with the Strasbourg Pass--which you can purchase in the Tourism Office in Cathedral square for 10.60 Euros and which gets you free admission to the Cathedral's other attraction, the astronomical clock's parade of the apostles, as well as one free museum admission, a free boat ride, and a half price museum admission of your choice. The pass is good for three days and represents a good value.
I recommend climbing the cathedral spire early in the morning, before many tour groups get going. It's difficult to pass people in the narrow spiral of the staircase, and it only gets hotter as the day wears on...
