It's not a perfect solution by any means, but if you are on PC, you can see your latency by loading Resource Monitor (resmon from search/run box), and expanding the TCP section and looking for the ffxiv entry.

Otherwise, you can just ping the lobby servers to get some idea. This can be done from a DOS prompt (cmd in search/run box) or from the terminal/tools screens in your routers. The registered DNS names currently assigned to the servers in Canada:

neolobby02.ffxiv.com
neolobby04.ffxiv.com
neolobby06.ffxiv.com

(ones in Japan use odd numbers 1, 3, 5)