The analog hygrometer can be stuck to the back wall of the viv, so you can see it looking in. I know science has an ideal location to get the best sampling for overall humidity, but I'm sure anywhere will be fine. At least halfway up I'd say.
If you're getting a corn snake (or some other colubrid), then regular room temp is probably fine for the cool side and you won't need a probe to keep such a close watch on the ambient temps. You'd be better off with a battery operated indoor thermometer from Walmart. No probe, just put in in the viv or leave it outside it, there's not a huge difference in temps inside and outside the viv. Some are a temperature/humidity gauge combo, those are nice. I use
THIS. It's huge, but I really like it. The daily hi/lo is nice.
We use thermometers with the probes to get a precise reading where the snake will make contact with the hot spot, which is important for the electronically-controlled heat source since too hot or not hot enough could cause issues. (The thermoSTAT probe is the primary temp gauge, the thermoMETER probe is backup, making sure the 'stat is accurate).
The UTH should only cover 1/3 to 1/2 of the bottom of the viv, with pretty much everywhere else in the viv being "cool", or cool
er anyway. The cool side floor of the viv should be about the same temp as the air temp (as long as your UTH isn't too big or too close to the middle).
If you've got it and you're set on using it, probably stick the probe anywhere opposite the UTH. The snake makes direct contact with the floor, so you can put the probe there. After a week or two, you may find you don't need it if the temps stay in a good range, and they probably will.