For example, almost 20 years after the fall of the Berlin Wall, we have 56,200 military personnel based in Germany. Doing what, exactly? Protecting Germany from whom? France? Poland?
We have 33,000 troops in Japan, another expensive country, and 28,000 in South Korea.
Here's the strategic conundrum about having foreign bases with fairly large numbers of troops instead of either a huge number of troops, as during the Fulda Gap years or just a caretaker staff to keep the base in shape in case it ever becomes needed. In case of war, we could easily fly in that many troops in a couple of days (the military has plans to borrow the fleets of Fed Ex and the big airlines, so restocking Germany would be, say, 112 flights of 747s), assuming we maintain air supremacy over the oceans.
Now, you might say, that's a Big If. But, if we've lost air supremacy over the oceans, well, then these poor bastards in these forward bases are dead. So, what's the war-fighting reason for deploying only moderately large numbers of troops overseas? It sounds like we have, in the unlikely event of a central European war, not enough troops in Germany to win, but, instead, just enough troops to suffer the worst defeat in American history.
Moreover, in a number of countries, most notably South Korea, leaving would do more for American popularity than anything else imaginable. For example, Seoul is a horribly overbuilt city with a gigantic green space in the middle of the city — the U.S. military base, which we could simply give to the nation of Korea to become the Central Park of Seoul. Moreover, as Dennis Dale has pointed out from his Army service in Korea and Okinawa, thousands of horny 20-year-olds don't make the most diplomatic ambassadors for America.
The most overlooked cost-saving would be unilaterally granting independence to Puerto Rico, because we spends tens of billions each year bribing Puerto Ricans to stay home. PR no longer even has a Navy base. In the long run, the key American ally in the Caribbean will be the naturally dominant country, Cuba, making PR even more dispensable.
Maybe, it would be easier to start over with figuring out which overseas assets are truly useful. For example, Diego Garcia, the fortress island in the middle of the Indian Ocean is highly useful, and inexpensive because it's uncontested, having no real indigenous population.
Similarly, the various bases the U.S. has in friendly countries around the Persian Gulf, such as Turkey and Bahrain, seem well worth the price of guarding the flow of oil from the greatest prize in world history.
After that, well, there are a lot of refueling bases here and there, which shouldn't cost too much, and can be left with skeleton crews in times of peace.
So, what do we really need and what do we really not need?