There really isn't given the conditions you've applied. The cheapest way to get between two data centers is wireless, however this will add a significant amount of latency (3+ms) to the connection. You can get faster wireless solutions, but in my experience that means they will need to be band licensed/microwave and the hardware for both sides will probably cost ~$20,000 and you'll have to either rent spectrum from someone or get it yourself from the FCC. The fastest way (latency wise) to connect them is to trench fiber between the two, costs will vary for this but if there isn't conduit already existing it can be in the tens of thousands to do this, just for 100m.
So to exactly answer your question, no there really isn't a cost effective low latency solution. That being said, if ~3-6ms isn't a huge deal you could probably rent roof space at both DCs (usually this can be done for a small fee, in the 100s/mo) and get long range carrier grade wifi gear to connect them (will probably be 2-3k$). If that latency is really too much you'll probably be stuck trying to find someone who has a Metro Ring in the area and seeing if you can hop on/off between the two facilities without having to route through a CO somewhere. That would be much lower latency, but probably pretty costly depending on how much bandwidth you need.
You had some other questions in there about what causes latency, that is probably best saved for a separate question as it applies to general networking. However to briefly answer it, most of the time it is the speed of light. Once you enter a facility the switching and routing is usually done at wire speed and thus doesn't add a significant delay. There are some edge cases like DSL and wireless that have serialization delay where the signaling done on the wire adds some significant overhead, but this is uncommon in data center situations where its usually SONET/ATM or ethernet.
To give an example in a well connected exchange like an Equinix data center you can get to any ISP in there and outside of the building in <1ms.