We've recently been recipient to an increase in spam and I'd like to determine the IP that the spam is coming from. My hope is that it will be coming from a limited number of IPs that I can manually block.
The "Received:" headers on the message will give you the source server, as would Exchange's Message Tracking functionality. Having said, it's hopeless to think that you can prevent any significant quantity of spam by manually blocking the IP addresses of SMTP servers sending you messages if you're receiving mail from the Internet.
You'd be better off looking at a third-party hosted or on-premise anti-spam solution, or at the very least, looking at the anti-spam functionality built-in to Exchange (meager, though it is). You absolutely don't stand a chance of keeping up with blocking spam manually.