According to a source in FamilySearch, all of the official FamilySearch/Family History Centers across the world, approximately 4500 of them, will get Library Version access to Ancestry.com early in February. To find out if there is a Center near you, go to the FamilySearch.org website and click on the FamilySearch Centers link at the top of the start-up page. If a Family History Center is listed, it will be given free access to Ancestry.com's library edition. This is the same edition currently available only in the larger Family History Centers.
It should be noted that FamilySearch is still in a period of transition in the naming of the Family History/Family Search Centers. I would assume that at some time in the not-to-distant future, all of the present Centers will be re-branded as FamilySearch Centers. But I have not heard anything official about a change in the names.
A search on the FamilySearch.org website in my area shows 10 centers in Scottsdale, Chandler, Phoenix, Mesa, and Paradise Valley as potential sites for the expanded program. This includes the Mesa Regional Family History Center (Mesa, Arizona Large Multi-Stake Family History Center which already has access to the program.
I am certain that the Centers will have to look at expanded hours to accommodate the increase in visitors access to Ancestry.com will bring.