Monarchs are probably the most familiar insects to the general public, as they are often used in schools as examples of biological phenomena like metamorphosis and mimicry. They are also large, colorful, and (at times) plentiful, so they are easily noticed even by people whose eyes are not tuned to insect movements.
Unlike most butterflies, Monarchs are fully migratory. In the fall, the eastern population migrates to wintering grounds in central and southern Mexico, while the western population retreats to southern California. In spring, these routes are reversed. No individual Monarch completes the entire round trip. Rather, females from the wintering population lay eggs in February or March, and subsequent generations complete the northward journey.
As with birds, geography influences Monarch migration. The best places to see large numbers of Monarchs at once are at southward-pointing peninsulas, like Cape May Point in New Jersey. Sometimes the air will be so full of Monarchs (and dragonflies!) that it can be hard to pick out birds from other flying things. One of my most memorable experiences of Monarchs was at Point Lookout State Park in Maryland on a chilly October morning when thousands of Monarchs were gathered at the point of the peninsula as they waited to warm enough to continue their journey. Migration occurs across a broad front, however, so you may see increased numbers in other butterfly gardens as Monarchs migrate.