Does routing distance affect performance significantly?
The Short Answer
Yes
The Long Answer
It may not necessarily need to be right in the country you are targeting - just a close region could be sufficient.
A good start is to determine where the major internet backbones/intercontinental links are in relation to your target audience, and plan accordingly. This way you could position services in a more advantageous position for future expansion. You can also choose to locate in adjacent countries that have lower hosting costs.
You can do this with maps such as this:
Regional Internet Map http://www.telegeography.com/product-info/map_traffic/images/inset.gif
Global Internet Map http://www.telegeography.com/product-info/map_internet/images/internet_map09_sm.gif
(source: telegeography.com)
blah http://www.telegeography.com/product-info/map_internet/images/im09_europe.gif blah http://www.telegeography.com/product-info/map_internet/images/main-projection-2010.png
If your target audience is actually china, then you have other problems to worry about, due to their extensive fire walling of traffic, if your application uses anything but port 80, with a fairly standard traffic pattern, then it will likely be blocked.
Where ever you host you may want to run a series of tests (latency, bandwidth, reliability) to and from the networks where your user base resides.
Ask your host for monitoring logs , if they cant or wont provide it, don't even consider them.
Don't be fooled by marketing hype, get to talk to a techie and see what level of global transit they have, the number of private peering points they have.
Also, worry about the speed of light, if your hosting on the other side of the world, your latency will be pretty bad, and you'll more than likely feel the full force of any global routing problems that occur.
I so wish I could see the pretty graphics that got deleted ;-(