Thermostat Location Costing Us Money?

I finally figured out why our upstairs bedroom feels so cool - cold actually, when the thermostat is set on 78 or 79...even 80. Our upstairs thermostat is located in the upstairs hallway; there are no A/C vents there, and most of the upstairs doors are normally kept closed, keeping the cool air mostly out of the hallway. The thermostat is reading the warmer temperature in the hallway, so the A/C stays on, and when I go into our bedroom, it is FREEZING (in my opinion, anyway). The downstairs is all open, so this issue does not exist there. What to do? Relocate the thermostat to our bedroom? I wonder if anyone else has this problem? It's hard laying in bed listening to the A/C unit churn on and on all night while I lay there freezing.....especially when I am anticipating electric bills in the $500 and $600  range.