Solid State Relay, but in reverse (AC to control DC)

Are there any types of Solid State Relays that will send a HIGH or LOW DC logic signal depending on if there is or is not an AC signal/current going thru it?

In a word no.
There are plenty of was to do that but an SSR is not one of them.
The best bet is to use an opto isolator and light the LED with a high value series resistor and a series diode. Then feed the transistor side into the arduino.
This will be an on/off signal at the mains frequency, so you might want to either smooth it or look in software to see if it is still pulsing.

You don't mention what magnitude AC you have in mind.
There are DC output SSRs.
Remember: rectifed AC yields DC, and, given the small current draw of the SSR input, you could probably get away with one diode and a modest smoothing capacitor.

Just a thought.

basically here is the idea. i own and operate a motel and am putting together an Arduino Mega system that will automate the motel lights and such with solid state relays (going thru a certified electrician to make sure everything is properly rated and can handle the loads).

There is a light switch in the office that turns on and off an outlet that has the ceiling fan + office lights plugged into it. When I turn off the office lights, I am usually also closing the office either for a few minutes to hours while I go into town shopping. What I am looking to do is have that disconnection of power send a signal to the Arduino Mega to let it know "the office is closed, shut off any lights and signage that are hooked up to the Solid State Relays.

I am thinking that the easiest, but perhaps not very practical, method would be to just have a low power wall wart that outputs 5V DC connected to a barrel connector, a resistor to lower the current, and then connect the current limited +5V and GND from the barrel connector to GND and a digital input on the arduino. If the light switch is turned off, the wall wart gets no power. If turned on, the digital input read high.

Why didn't you tell that in the first place? (:

I come from the "Clue" school of not telling long winded stories.

Butler: "To make a long story short"
Col Mustard: "Too late"

There are mechanical relays with "ac coils", too. You could use the contacts as you would any switch as an Arduino input.

I come from the "Clue" school of not telling long winded stories

In which case you get short winded answers.