I'll nominate Great Basin National Park, signed on I-80 east way back in Fernley, Nevada, about 350 miles away, give or take a few. Street View image:
(https://www.aaroads.com/forum/proxy.php?request=http%3A%2F%2Fi.imgur.com%2FdBGvkle.png&hash=1351f84e5c4c35d59f299a2b7bc5bdad3c95babf)
Non-freeway guide signs welcome, too, I suppose. Might the Grand Canyon be signposted farther away?
I can't think of any offhand, mainly because Nevada seems to be a unique geographic example. a sparse road network, and here I-80 swings northeast where US-50 (via alt US-50) heads east to the park.
I believe that Yellowstone is signed from I-90 in Sheridan, WY but that's only about 160 miles.
Delaware Water Gap doesn't count.
I could've sworn there was a Yellowstone Nat'l Park sign in Nebraska on one of their upcoming attractions signs they have up and down I-80. Since I just got done driving much of this EB the other day I would not have seen it but I drove it WB in 2010 which is when I thought I saw it.
The closest I can find on street view now is this location (view in new google maps then dial back the clock a couple years) which very recently was replaced with a sign that does not mention it. This is 40 miles east of Ogallala, or about 640 miles via US 26 as they suggest.
http://goo.gl/maps/mhd0A
Mapmikey