On or very near the grill surface, reason being you want to know the temperature in the zone of your food.
Lid thermometers can be inaccurate. So to me, they become more of a reference, not a gospel of the true temperature where my food is cooking.
Most go by the internal temperature of the item being cooked. But my experience has really varied with that.
Also, and this comes from a lot of experience with temperature monitoring and controlling devices, thermometers will vary, often a lot. At the level most come in for culinary and home BBQing, accuracy is vague until proven. One "standard" which works pretty well is the Ice Water and Boiling Water tests. It tells how accurate a given thermometer is at those points. But is not an absolute. Elevation plays a part in accuracies.
But Industry Standards are not practically assumed at the home level of our BBQ's. So finding the "sweet spots" are more a learned thing.
Test your internal BBQ hood temperature against your monitoring thermometers. My SIL's new Weber is pretty close to my ThermPro TP-8 I use as my go-to for my smoking/cooking. It's running ~10 degrees hotter.
For my use, the hood thermometers give me a reference of the progress because the hood temperature begins rising as less steam is produced. Like starting out at a reading in the 320's, then later on climbing into the mid-300's or even hotter. When I start seeing hotter temperatures, experience has taught me that the meat is getting more done.
This is based on gas grilling, and leaving the burners at a set point. For knob fiddlers, accuracies will lurch all over the map. I usually set at the lowest setting, then shut off one entire burner to reach a lower temperature if things get away from my low and slow cooking.
So the hood thermometer is best as a reference. Not as an indication of absolutes.
As you get to know your grill, you will learn it's peculiarities.