Is that store open today?
I don't know, you should call X to find out.
Is the expression to find out correct? What similar expression can I use in place of to find out?
Find out, which means to learn a piece of information, is the best verb to use here.
In its place, other expressions would be: and ask, and ask them, and/to check, to be sure, or to make sure.
In this context we can assume that the person aiming to find out will be talking to a person on the other end of the phone (as opposed to a service)
Thus, some alternatives:
I don't know, you should call X to ask.
I don't know, you should call X then you'll know.
I don't know, you should call X then you'll find out.
Though in this context these wouldn't make much sense without reconstructing the sentence, the following are good replacements for "to find out":
Discover (You can call X and discover)
See (If you call X you will see)
Unearth (If you find the directory you might unearth it)
Come across (You might come across it in the directory)
Get (You can get that information from the Internet)
You have a wealth of choice :)
EDIT: Shawn however does make the best point, that what you have already is the best phrase to use in your example. :)