There are at least two major costs of being the world’s only superpower.
One of these costs is monetary. It costs a great deal of money to do all the things required of the US as the world’s superpower. We have to spend much more on our military than anyone else does. We have to spend on foreign aid. We end up having to fight in wars like the Persian Gulf War of 1991 or the recent invasions of Iraq and Afghanistan. These are things that we would not have to do as much of if we were not a superpower.
The other cost is in our international standing. Because we are the world’s superpower, we are something of a target. For example, China resents our power in its region and therefore has strained relations with us. It is also our status as a superpower that causes us to end up in conflict with countries like Iran. We could have better relations with other countries if we were not a superpower.