What's a good way to connect to a large number of nodes? Is there some way I can get a list of nodes, preferably distributed all over the world?
Add addnode=<ip> entries in bitcoin.conf, or use the addnode=<ip> argument in command-line, if you want to connect to more than 125 nodes (
https://github.com/bitcoin/bitcoin/blob/master/src/net.cpp#L64), then I think you will need to change -maxconnections=<x> to something higher.
Blockchain.info is very well connected so you could add some of the nodes they are connected to:
https://blockchain.info/ip-log