If I go down to a Blue Jays game, I definitely look at the pitching match ups, and the pitchers who are pitching to determine the game I go to. For example if I'm looking at going to catch a Jays game when the Mariners in town, I'll for sure look out and see if Felix Hernandez is pitching one of those games. If he is, I'm going down to that one over the other two.
Also, when Josh Towers pitched during 2005, I'd try to make it down to everyone of his home starts. Now I went to many other Jays games that season that he wasn't pitching, though since he was my favourite player I tried to make it to every game he pitched.
As for watching games on the road, I'll go and watch a game at any ballpark regardless of who is pitching or not pitching. Also, since when travelling, it's tough to schedule out approximately on which pitcher you want to see unless you stay in town the entire week.