Buy a cheap laser or for that matter any flashlamp with a decent beam. Move some measured distance from the base of the building. Point the laser at the top of the building and measure the angle that the laser/flashlamp is tilted. A simple trig calculation, using the length of the laser and the distance it is tilted, the accuracy can be increased by intercepting the beam a couple of feet from the ground. The tangent of the angle and the distance from the building will allow its height to be calculated.
Best done at night but be careful to avoid being hit by a barometer that some idiot has dropped from the top of the building
So you don't risk environmental contamination from the mercury inside the column (inherent in many of these suggestions), then go down to the local building department and pull the blueprints for the building.
You could use the GPS in your cell phone to get the height of the barometer above sea level while it's on the roof, then put it on the ground and get a second reading, then just subtract the two.
You could throw the barometer over the building and then calculate the trajectory and the time it took it to land on the other side, but the math required to do that is way too complicated for me to figure out.