Where did the Spanish American war take place?
All significant fighting in the Spanish-American War took place in two locations. These were Cuba, where the main fighting occurred, and the Philippines. Most of the land fighting of the war took place in Cuba. Cuba was the cause of the war in the first place as the US was trying to help Cuba become independent of Spain. The US attacked the Philippines simply as another way to weaken Spain. There was one relatively major naval engagement and some small land battles there. The US also took Guam and Puerto Rico in this war, but both of these were essentially bloodless conquests.
I would like to expand upon the above answer by naming four places prominent in the Spanish-American war in decreasing order of importance due to the amount of time actually spent in battle. The four places are as follows: Cuba, the Philippines, Puerto Rico, and Guam.
Generally, the Spanish-American War was just what it says: a war between Spain and The United States of America. It happened as a result of American involvement in Cuba's quest for independence. (The United States ultimately demanded Cuba's independence, and Spain rejected that idea with a declaration of war.) The war was ten weeks long and generally fought in "the Caribbean" and "the pacific." However, we can be more specific.
Cuba: As the above answer correctly indicates, the majority of the fighting did take place in Cuba. This would make sense, since Cuba's independence was the original reason for the war. First, it is important to mention the sinking of the USS Maine right in Havana harbor. Its sinking is considered a "mystery," but added to tensions already there. There were many battles fought on the mainland of Cuba, therefore securing a large land campaign and naval campaign. Eventually, the US had to withdraw most of its troops from Cuba due to a severe outbreak of yellow fever.
The Philippines: Although much of it had more to do with European forces than American forces, the Philippines was also more grounds for battle in this war. (One has to be careful, though, not to confuse the bloodshed of the Spanish-American War with the Philippine-American War (which directly followed the former). Still, the Americans fought and one the first battle on Manila Bay against the Spanish. Other European forces became involved as well, and eventually Filipino forces took control over most of the islands and finally declared independence after the Battle of Manila. (Unfortunately, because of a miscommunication about a ceasefire and a refusal to allow Filipino forces to enter Manila, this eventually caused the Philippine-American War.)
Puerto Rico: When the American's navy attacked San Juan, Puerto Rico and established a blockade there, the successful assault was followed up by a land campaign and, after a few battles, Spain gave up Puerto Rico to the United States.
Guam: One of the lesser places that housed the Spanish-American War, Guam came into play when American forces "captured" Guam by sending only a few cannon rounds out and them being misread as salutes. (Guam had no idea there was a war.) Guam surrendered quite peacefully and was no longer Spain's issue.
Thus, the entirety of the Spanish-American War took place in those four areas.