I do recall that a possible mission for Andrew Jackson after his incursion into, and essentially seizure of, Florida was to likewise annex Cuba. Cuba could then be a staging point for other similar incursions into Spanish-held islands in the Caribbean in the early-to-mid nineteenth century. However, this would probably also be a catalyst for a civil war, much like the annexation of Texas was in OTL. Spain allowed slavery at this time, so there would have been a number of slaves already on the islands, making their entry into the union as states controversial. So the Civil War wouldn't necessarily be skipped, just the order of imperialism vs. ACW just switched in time.
It would be pretty tough, generally speaking, to come up with a TL where the US didn't have a civil war and still had imperialism, as the ACW is what really established the supremacy of the federal government over the states. Without a strong central power, you can't really have much of an empire.
EDIT: I had an epiphany as soon as I clicked the "post" button. There were also fears that Andrew Jackson would have marched on Washington, DC, if they had censured him for his actions in FL (ala Napoleon). Jackson was wildly popular with the people, so if he had staged a coup, there may not have been a popular uprising against him. This would have allowed Jackson to center authority in Washington w/o a civil war, and then he could have launched incursions in any direction he chose to establish a true empire.