Actually, there is Old Inspiration Point, New Inspiration Point and Tunnel View. Old Inspiration Point being on the original trail into Yosemite where the Valley was first seen by whites. New Inspiration Point is on the road (for automobiles) that replaced the trail, but before the tunnel was made, and of course the present day Tunnel View (which is not considered to be one of the "Inspiration" points).
One reaches New Inspiration Point by hiking up from the parking lot across the road from Tunnel View. From New Inspiration Point is a further hike up to reach Old Inspiration Point. Check out this trail guide (note the last paragraph):
While I have done the hike to New Inspiration Point (and continued to Glacier Point on a 4-day backpack trip with the 4x5), I have not been to the Old Inspiration Point.
And from the Yosemite NP website:
Descending towards the Yo-Semite Valley, we came upon a high point clear of trees from whence we had our first view of the singular and romantic valley; and as the scene opened in full view before us, we were almost speechless with wondering admiration at its wild and sublime grandeur.—James Hutchings, from an 1855 journal entry at Old Inspiration Point
Elliot, a good friend had a book published by Lodima. The story of its printing was quite entertaining, but the printing is of the highest quality.