JPHBUCKS has an excellent point. I am so thankful that we went to Amsterdam and had the privilege to see the Reichsmuseum, Van Gogh, Anne Franks House, and some other various sights. However, I won't go back because it's just too stressful to constantly dodge the bicycles in addition to the trams, cars, and busses.
Many people on this Forum recommend staying in a smaller city such as Haarlem or Leiden and then taking a quick train into central Amsterdam for your sightseeing, and I heartily concur. Definitely go to the Keukenhof! It's probably the most beautiful sight I have ever seen.
I spend most of my time in Belgium due to having friends there. For a first time visitor, I would suggest consideration of Antwerp, Ghent, and Bruges, but definitely also a day in Brussels to see the Fine Arts Museum, Musical Instruments Museum, and the Grand Place. A poster above mentioned the ease of trains in Belgium. This wonderful transport network allows you to base in one city (perhaps Ghent?) and easily do day trips to other places since Belgium is so small. These destinations are all in the Flanders region, but if you like scenery you can also consider the Walloon cities of Namur or Dinant. There is so much history packed into this small country that I'm still exploring it after 20+ visits.
I would also be remiss if I left out Ieper/Ypres, also in the Flanders region. The World War 1 sights there are a real eye opener for most of us Americans because our typical history study focuses more on WW 2. As noted regarding Ieper/Ypres most Belgian cities have 2 names, one in Dutch (Nederlands) and one in French. Sometimes the names are quite similar, but not always. If you're heading somewhere on the train or by car, those names will change as you cross the border from one region to another. Be sure you know both names or you'll think you're on the wrong train!
You really can't go wrong with any destination you pick in these 2 countries. Happy planning!