I don’t think these fit the OP’s definition of an exit sign but are rather furthest away you’ve seen a control city. Correct me if I’m wrong @Mesquite-oh but you are looking for a sign like “Bupkis Exit 102” and that’s 130 miles away. Right?
Yes you are correct. I was really looking for the highway exit sign with the farthest control city (city used by highway signs to indicate direction- thanks for the clue). Those “3000 miles to the other end of the highway” signs seem more point of interest signs than directional signs. Didja know that there is a detailed Wikipedia article on control cities?
How interesting!
I agree. The Wiki item makes it look as though Canadian highways don’t like to head for control cities in another province, but that’s not always the case: just east of Winnipeg, I’ve followed “Highway 1 East Kenora,” and in eastern Ontario, I’ve followed “Highway 401 East Montreal.” And in Montreal, I spotted a highway sign that was an on-ramp to A20 west with “A20 Ouest [i.e. West] Toronto” on it.
Driving north on Interstate 5 around Seattle, I got a kick out of “Vancouver B.C.” being used as a control city, but the best of all was when I pulled off I-15 in Shelby, MT, to gas up, and saw this when I was trying to get back onto I-15 northbound, back to Canada:
Hm. Well, click the blank image and it should load. For those who do not choose to link, it’s basically a sign that says I-15 goes northbound, and the next control city is Lethbridge, Alberta–yep, across an international border.
I see the Denver one all the time
Here in RI we got some signs for cities 15, maybe 20 mile away. We also got a place where it says “Welcome to Esmond” on both sides of the sign.
RI is small enough I bet there are a lot of those.
…and as we got on the highway, I could see my mom had something in her hand. “Mom, what you got there?” “Oh, nothing.” “Come on!” (more back and forth) “Ok, it’s the change for the toll for the Golden Gate Bridge. I just want to be ready.”
Leaving Phoenix west, there’s a sign “Los Angeles 340-(something)”, but it pretty much is the next destination. I guess you could want to go to Blythe, or Quartzite, but why? 
There might seem to be an internal contradiction in that statement but a closer look reveals something interesting. Even though Alaska is considerably larger than RI, given that a village would require at least one resident we could actually have more of them here Little Rhody than the largest US state due to our greater population.
It seems to be similar in New Jersey except I see fewer formal signs per se. New Jersey toward the coast reminds me in many ways of coastal Florida: a non-stop strip of development with endless suburbs that merge into each other. But in New Jersey, it seems that despite looking the same from block to block, the business will be labelled in one block as “Schmoeville bait and lube” while in the next block they’ll all change to “Janesdale bait and lube” with no other apparent difference.