Visit Lake Manyara and Tarangire
If you have an extra day or 2 in Tanzania and are looking for national parks to explore that aren't part of the Serengeti ecosystem, Tarangire and Lake Manyara are some of the best national parks in Tanzania that you shouldn't miss while you are here. Both Tarangire and Lake Manyara offer varying types of landscapes and animals that differentiate them from Serengeti and Ngorongoro Crater, making them worthwhile to visit. Tarangire is known for its abundance of elephants and baobab trees with a more hilly scenery unlike what you will find in Serengeti.
Lake Manyara on the other hand is known for its high density of baboons and monkeys as well as all kinds of colorful bird species you can see. Since the area is a little more foresty, it is a little harder to track big predators as they are often hidden up high in the trees most of the time.