I approach it the other way. Instead of following teams or riders, I try to do all I can to support local professional races. Financially successful races are at the heart of any professional racing circuit, so I visit the town, have a nice meal at a local restaurant, tell the locals I am there to watch the bike racing, etc.
These days I trek out to watch the Ladies Tour of Norway at the border with Sweden every August. It takes place in smaller towns, where a UCI pro women's race is a *huge* deal and the crowds are sizeable. As a result, I think the race is one of the most popular among the riders.