The Cubs will travel the fewest miles of any team in baseball. Just under 23,000 miles for the season. Below is the website that has the stats for all the teams. The Mariners will travel the most, even more than Arizona and LA., who had to travel to Australia. Looks like they make multiple trips to the east coast and Florida.
The teams that play around the great lakes seem to travel the least amount. Obviously, the teams out west travel more.