One of the most spectacular gardens in the world can be found at Keukenhof, located about one hour from Amsterdam. Keukenhof celebrates Holland's tulip heritage with these massive and beautiful formal gardens that are only open for a few weeks each year from late March through early May (visit http://www.keukenhof.com for operating hours and dates).
Think of Keukenhof as an "amusement park for flowers". There are meandering paths, fields exploring with color as millions of tulips are blooming, the site has the requisite windmill or two, as well as a variety of exhibits. Hint: The best viewing time is early April BEFORE they cut the tulips from the fields behind the formal gardens...it is a bit cold, so bring a jacket. You can also rent a bicycle here to explore the tulip growing area. There are also food stands, strolling musicians, a hedge maze, and demonstrations going on throughout the day. I'm not much of a flower fanatic, but I found myself staying for about 1/2 a day.
Keukenhof can be reached by car by driving to the town of Lisse on the N208 highway from Haarlem or Amsterdam. A more convenient way to get there is to take the train from Amsterdam Central Station or Schipol Airport (the trains usually leave every 10 minutes to Leiden (about 20 minutes by train). Upon exiting the train station, look for the bus queue and take the #54 bus direct to Keukenhof (service runs about every 15 minutes). When you buy your bus ticket (either on the bus or at the kiosk where the buses queue), the entrance fee to Keukenhof is included, so you simply step off the bus after the short 15-20 minute ride and walk into the main gate. When you're done, the return bus service follows the same route back to the train station (every 15 minutes).