Within the Schönbrunn Palace Gardens, there are multiple highlights to visit. One can spend hours just walking through the gardens. A favorite of mine is the Palm House (Palmenhaus*) which provides a lovely reflection of light against the green structure. If you visit to take photos in spring time, you can capture the surrounding greenery, a few water fountains, gardens full of flowers and the architecture of the Palm House. In autumn, the reds and yellows are also a sight to remember, and I particularly recommend the sundown hours for the special touch of the evening light.
*Note: the entry to the Palm House carries an entry fee.