Is there any such thing as "proof of location"? I'm looking for a way for someone to prove to me their geographical location without a trusted third-party. Imagine wanting to prove to someone you're actually physically in a specific place. I'd imagine you'd need something like perhaps a receiver of some kind to triangulate the location of a satellite that could perhaps only be calculated in that spot?

Is this possible?
A clear cut answer to your question is NO for now. In the literature there is no an accurate and reliable scheme that can determine geolocation of the data. They are basically timing-based schemes and the problem with timing (in this case) is that many factors can affect it. Also they usually assume that there are some reliable landmarks around the world that can help determining data location.

I think some internet infrastructures are needed to be improved to support such capability. See below for some paper in this area.

However, securing outsourced data might be a solution in hand rather than finding its location (I entourage you to think/read about why data location may matter). 

1-GeoProof: Proofs of Geographic Location for Cloud
Computing Environment:http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&amp;arnumber=6258199

2-Do You Know Where Your Cloud Files Are? :
http://dl.acm.org/citation.cfm?id=2046677

3-Geolocation of Data in the Cloud:
http://znjp.com/papers/gondree-codaspy13.pdf