finding the best network latency between two countries
You won't get this information just on one click. What you can try is to use many different Looking Glass servers and based on the information you get there you get some estimates. Here is a list of some looking glass servers. Another possibility is to use some traceroute servers. I recommend you to google for e.g. some famous newspapers in the regions you want to measure and then do some nslookup and with the IP addresses you get you can do some tests. This could give you some indications, but as Zoredache said it is not very reliable.
UPDATE: I doubt that you can automate those lookups. But maybe you can find a tool on this page.
There is probably no way to get an accurate estimate in a few minutes. Most downstream service providers are multi-homed, and everybody uses BGP based routing, so two individual customers who are physically very near each other may still get wildly different routing paths.
That said, you could probably create a rough guesstimate by:
Looking at the Submarine Cable Map. Almost all long-haul cabling is run under the sea, and this map gives you a good overview of which areas are well connected.
Sitting down with Microsoft Excel, a long list of looking glass servers, and building up a large'ish latency data set yourself.
Talking to other network professionals in the region you're interested in.
The Internet is not connected by country, almost every country has more then a single link. The link that is chosen depends heavily on both where you are connecting from, and where you are connecting too.
You could pick an ISP that is great for some users in a country, and horrible for others.
The issue is far to complex for a simple tool to give you some kind of guesstimate. The only way to be sure would be to test. You could try and get potential ISPs, to perform a trace-route for you to various network providers in the regions you are curious about.
I've been looking for similar information, but for private networks. I found this link which might be useful, it demonstrates the latency between sites on Private VPNs with Verizon. Verizon IP Latency Statistics