Arrive early.
The best stages to watch are the mountain stages, as riders are moving slowly, and they tend to get spread out more which gives you more to watch. For the same reason, time trials are good events.
Make sure you arrive early. They close the roads to cars hours before the riders come through on the mountain stages. If you're on a bike they are a bit more lenient, but they will stop you riding before the peloton arrives.
The caravan (publicity cars throwing out freebies) comes through about an hour before the riders. The timestable with expected arrival times is published on the official website before the event so you will be able to plan your schedule pretty well.
If you are following the event, its also good to go to the start/finish of a stage as you get to mingle pretty closely with the riders, teambuses, mechanics, etc. If you get lucky booking your hotel, you can even get to meet the riders.