I am looking to figure out what my IP address is from a console application.
I am used to a web application by using the Request.ServerVariables collection
Request.ServerVariables
The System.Net namespace is your friend here. In particular, APIs such as DNS.GetHostByName.
However, any given machine may have multiple IP addresses (multiple NICs, IPv4 and IPv6 etc) so it's not quite as simple a question as you pose.