You can set up local BGP routers and peer them and play with it.

Another fun thing is to log into publicly available looking glass servers. Most ISPs (including very, very, very large ones) operate routers that have their full view of the BGP routing tables. They either run web interfaces that let you query those tables (more common) or make public ssh or telnet credentials to log in with roles that have very limited access to the available commands, but have read rights to those tables.