You will end up with better gas mileage overall, but not at first. The reason for this is that Nitrogen does not expand and contract like air that is normally used to inflate tires. The water that is in the air that is in tires normally expand and contract with the change of temperatures outside. If you notice that in the winter your tires look like they have lost pressure and seem flatter than when they were put on. And in the summer you seem to have to remove air at times because they seem to have over inflated. That is because the air inside is being heated up and expanding allowing the tire to seem that it has become more inflated.....it actually has, but that is because of the water that is in the air normally in the tire.
As for Nitrogen, you will be hard pressed to find a shop that has Nitrogen to inflate tires. It is WAY too costly to use on a normal basis. BUT, if you find one I would spend the extra money to have them inflated with Nitrogen.....but GOOD LUCK finding one.