vapor barrier question please

Howdy, I am setting up a room in my garage. The climate is hot/humid in summer and much of the year, and mild to cold and dry in winter. It never freezes. I have built three walls off the existing block wall. These are made from 2x4's. And will be covered in drywall. I plan to insulate this space using r13 fiberglass and cover the block in foamboard and drywall. I am trying to not build a ceiling and use the existing one. I will use styrofoam and plywood as a floor. The entire space will be air conditioned. Do I need a vapor barrier on both sides of the new walls, and where would it go on the floor if needed. The existing ceilng is plastered drywall with sprayed loose insulation. I have no idea of it's "r" rating. Will this pose a problem thatwill require a ceiling to be made? Thank you in advance.

I would....
Install insulation bats(kraft paper in of course) then hang plastic sheeting for vapor barrier....3mm or 4mm before installing shheetrock. The Vap Barrier is code here on ext walls.

Certainly wouldn't hurt to do this between the block and studs either....it would just be extra protection. Be good to keep moisture off the crap they sell as lumber nowadays.

Ceiling material sounds fine no need to drop another set of joists in......though it would be easy to do since you could frame in pockets in the new stud walls....
So most importantly, if you think you need the ceiling now is obviously the time.

As far as the floor goes, I assume it is a concrete slab and should have had a vapor barrier installed(per code) between the compacted gravel base and the concrete prior to pouring the floor.....if it is.......pre 90's it may or may not have this depending on where you are...I wouldn't think you need to worry about.

Hope that helps.....
-OitW