Probably Facebook hide the Admin of a Page for a good reason. But some times you need to get in contact with them for what ever reason. There is one way to find them not inside Facebook but on there Webpage . Most Brand Facebook Pages have a Webpage too with some Facebook functions LIKE Comment or some more advanced code running .
There you find mostly the Admin of the Page too as FB Webpages need the Meta tags there is the Facebook ID of the Admins that mostly 99% also Admin the Page inside FB .
view the source code and search for following Meta tags. There is at least the developer listed and also the admin to moderate comments and admin the virtual fanpages generated by likes and comments.
UPDATE : Since Facebook introduce the massage button on Fanpages there is no real need to find admins as you can get in contact simple by sending a massage.
If the page is huge it could be that you dont get a respond. There is one more option since many pages use auto FB ->Tweets to get in contact via Twitter. All pages use the Facebook own short url service fb.me simple make a search for that url. Dont fall with the door in the house try to get first some relation and trustfull contact before your formulate your needs.
Geotarget Fanpage Search if you want to limit the search to a special region you can add geo cordinates to the search to . there is a smal tool GEO Tools in the sub menu on that blog to use any service that provide longitude and langitude coordinates from maps with some string examples at the bottom.
Add the search term + geo paramter into your tweetdeck search
Admin by ImageTag : Last option is look on the page for Tagged images mostly the admin is the first person who tag on a page under the tagged name you will see who is tages him Franz Zucker . Chances are very good to see name of Admins
The Numbers at the end represent the FB ID of the Admin , find him on FB with the profile Link
Profile Link : http://www.facebook.com/profile.php?id=XXXXXXXXXXX
There can be one or multiple Admins on the Page in our case xxx.. and 1234 2 Admins are on the Page. These technic only work if the FB PAge and Webpage is done by professional not on random Pages . Mostly at least the owner of the page and a coder will be admin there.
Why you could contact a Facebook Admin if you find interesting opportunities to cross collaborate with a Fanpage Admin it could be interesting for both . Its a nice alternive than only push Facebook adverts to gain new Fans . Often Pages are not direct copetitors as they have different regions and produkts or Services it brings more value for the Fans and the Page owner.
One last thought dont ask for basic Link posts to your page that would not work be more creative make a content partner ship or even games that run on 2 or more pages . The more time and clicks the user make on your Fanpage the higher EdgeRank and visibility it will get .
Still some question just add it to the comment