Unlike daffs, tulips tend to decline every year in our climate. They apparently only really like living in Holland. Also their flowers don't last quite as long as daffs, and their foliage is not as nice. The Rube prefers daffs.
On the other hand, they are quite diverse in form and color. The Main picture, taken in the Haupt Conservatory, has the classic tulip flower shape that kids learn to draw. Fig. 1 is also from the Conservatory, Fig. 2 are in the formal gardens just outside it, and Fig. 3, the shortest tulip the Rube has seen (red flowers at right of photo), is out in the Rock Garden.
When you visit the New York Botanical Garden, you can pay either $3 for the grounds and then a couple of extra dollars for each of the special attractions (Conservatory, Rock Garden, using the Tram, etc.). Or $10 for the Garden passport. The Rube would recommend the latter if you get there early and are planning to make a day of it. Ask for a map if available. Then go to the tram stop and take the grand tour until you get back to where you started, circling the areas you want to walk to. Do not miss the Conservatory or Rock Garden!