The other day I was just outside of Baltimore when I saw road signs on the highway giving me the distance to New York, which is relatively far away. A few days later in the same region, I saw a sign that had an arrow and “Texas”. That has to be the farthest road sign I have ever seen. I’m in Baltimore and I see signs for Texas. And it didn’t give a city. It just gave the state. Also, I’ve heard of signs in Eastern Ohio that give New York as a control city. What are signs like that you’ve seen?
I haven’t seen it personally, but this is allegedly (one of?) the most extreme ones in the USA. It’s in Ocean City, MD at one end of Highway 50.
Strangely, at the other end you get this one.
Where did the other 36 miles go?
Yes, that’s on the bridge as you leave Ocean City. I’ve seen it many times. It’s always good for a giggle on the way home from vacation.
As for the OP, along I-95 North in Baltimore, New York is the default city listed. The signs also mention Philadelphia, but New York seems to win out. Along the entrance ramps, it almost always says,
“I-95 North
New York
Philadelphia”
I always thought that was a little odd - Philadelphia should be listed first, since you’re going to get to Philly first.
Texas, MD is a small town in Baltimore County. You drive through it without even noticing you have left Hunt Valley/Cockeysville and into Timonium. There is also a California, MD.
Leaving Wilmington NC there is a sign for Bakersfield CA at the other end of I 40.
There is a similiar long distance sign on I-70 W leaving Baltimore. It has four cities and distances listed.
Columbus 420
St.Louis 845
Denver 1700
Cove Fort 2200
It’s possible that over the years route 50 has changed a bit and one side has revised their sign and the other hasn’t.
There’s one in Gettysburg, PA that has the mileage for Gettysburg, SD I think. The sign is really small and in the middle of the city so I don’t remember what it said exactly.
Thought I posted this 
US 41 ends/begins near Copper Habor, MI.
In town there is a sign that says something like:
Calument 35
Houghton 47
Miami, FL 1990
I had a pic of the US 41 end sign, but it seems to gone from the net.
Brian
Nowhere; that picture (of the sign in Sacramento) is of the old sign; the new one matches the Ocean City sign. It’s also telling that the old and new sign have the same distance, except for the reversal of the last two digits. Mistake? Prank? Or intentional change?
I’m looking out my window at US 41 right now. But I’m a little closer to the southern end of the road. FYI it’s also called the Tamiami Trail since it goes "Ta Miami."
I’ve also seen the road sign for Sacramento at Ocean City, MD.
In the interests of research, I plugged both cities into Mapquest.
Ocean City, MD, at N Philadelphia Ave and 4th St, to Sacramento, CA, at 10th St and I St (at Cesar Chavez Park) is listed as 2859.5 miles. The reverse route (same end points) is 2863.5 miles.
So what happened to the other 200 miles???
Ah. Mistake.
In case people missed it up there, Madd Maxx solved the mystery of the OP’s “Texas” sign.
You can see plenty of similar ones in the UK, with signs pointing you to California, Washington, New York, Quebec, and so on and so on…
The bellboy stole it.
The bellboy’s name wouldn’t happen to end in -GRY, would it?
There’s this one, although, to be fair, it doesn’t say how far:
And just north of California, MD is Hollywood, MD. And I’m just a little north of that. 
Not quite the same as the OP, but:
Heading east across the Bosphorus Bridge in Istanbul, you see a sign that says “Welcome to Asia.”
“Asia Next 12,000 Exits” would be funnier, though.
The sign had a longhorn on it.
We’ve been there on our way down to the beach. 
I read a long time ago (and it might even be true) that distances on maps and road signs are pegged to the main Post Office in town. So, if the main post office in Sacremento was moved from one side of town to the other, that would change the mileage. By 36 miles? I don’t know; how big is Sacremento?
I’ll spare you the list of “distant” towns in Indiana.