Home Depot, etc. sell 1/8th" hardboard in 4x8* sheets for about $12. It's very light and somewhat flexible while smooth on one side. If you want a nice backing, I would recommend that stuff. It's also stiff enough to frame around. Or, it's also stiff enough to mount without any kind of frame (just drill through each corner and screw to the wall. You could mount the map to the hardboard with tape, glue, tacks, or whatever.
Fix the map to the board with blue tape along two edges for square, then trace the other two edges and cut off the excess. Clean the board, then affix the map with stuff.
Presto. Frame or not, your choice.
*you would lose 1" along the short side.