We need to find the closest possible hosting location on the internet
(in terms of IP roundtrip) to a specific IP address which runs a web
service we consume.

The hosting location could be with a hosting company, or even just a
domestic ADSL line, we don't care- we just need to get the ping times
to the destination IP down absolutely as low as they can go because
the performance of our software is being affected.

I can't tell you much more about it on a public forum, but I am
willing to pay the right person to do the job.

If you are an expert in this area and have experience solving this
kind of problem, please email me with your experience/qualifications.