Thermometer Placement

Place the damper as close to the stove as possible where it is easily reached.

Stove top thermometer is usually on the step top to view from a distance.

I don't think the temperature will read much different before and after the damper. It just slows the velocity in turn reducing the volume left up the stack. Like a throttle. The air adjustment determines how much air is available for the fire.
I put the damper so close to the stove, there's no room for the thermometer before it. I only measured temp there when designing baffles, and can tell you the temps are far higher there without a baffle plate. The object is to know you're keeping the stack temp high enough where it enters the chimney to prevent condensing below *250 all the way up. So the temp you need (or the LOSS you need) varies on how much is needed to heat the inner flue. The flue diameter and absorbstion into the chimney if masonry, if not insulated or lined determines the temp you want going up. Time will tell when you keep it hot enough to stay clean. Running too cool can form deposits quickly, so check often until you know how much heat is needed to be left up in your individual case.

Good stove temp, I assume they will read about the same with the thermometer still located between the stove and damper, so yes it will be about the same as stove temp. (and may be sensing heat from stove) With my insulated interior stainless 6 inch X 10 foot high chimney, I try to run 300 to 350* on pipe just before chimney. Mine doesn't need to be hotter than that. It should be easy to move your pipe thermometer to see what you're temp is higher up. You should record these temperatures mid burn so you know what changes do. A baffle in the stove should allow about half the temperature of the stove top at beginning of chimney flue. Again, flue temp you need depends on the chimney. 300* may be fine for a short insulated chimney, but it would be no where near enough for a large masonry exterior flue. A sensor a foot from the top is the only way you're going to know when you're leaving the exact amount up. During the cycle of a burn this is going to vary widely.
I stress a baffle because it decreases smoke. Decrease in smoke decreases particles that form creosote.