Something is draining my battery, have symptoms if you have possible solution!

What is your question?

Four weeks ago, I left NC to travel to IL. That morning my car didn't start. I turned the key and all the lights/radio/air came on, but I only heard a clicking noise from the engine. We jump started it and then I drove the 14+ hours to IL. Four days later the car needed to be jumped again. I had double checked when I parked it to ensure no interior lights or functions were left on. I then drove it to MN (a 8 hour drive) and within three days it needed jumping again. But then, after driving between the Twin Cities, about a 50 minute drive each direction, I let it sit overnight and the next day it started just fine. Now I've had to jump start it again. I had someone from AAA come look at the battery (which was purchased through AAA in 2013 and replaced in 2014) and they said it was a good battery but that something was draining it. (Yeah, thanks.) Now my question is: I've seen a couple different places that it could be the FSR (FSU?) and I think I can figure out how to replace that. I had noticed on my drive that at some points, even though I had the air conditioning on and only blowing through the top vents, I could feel heat on my feet. I had just assumed it was from sitting for too long and stopped to walk around when it happened. Could that be what people mean when they're saying that the air conditioning system acts funny when the FSR needs replacement? I unplug my GPS center and turn everything off (air and radio included) when I get out of the car. I'm not leaving any lights on or doors open. It's draining practically overnight at this point and I'm two days away from just buying a trickle charger and letting it be, but I'd really like to fix the problem. Is it worth purchasing and installing a new FSR? Thank you in advance, and if you have any further questions please let me know!