If you're tight on days, Tarangire and Lake Manyara are the two parks travellers most often skip or compress. They're both worth visiting, but for very different reasons.
Tarangire — elephants and baobabs Dry-season giant elephant herds along the Tarangire River. Ancient baobabs. Fewer vehicles than Serengeti or Ngorongoro. Best June-October.
Lake Manyara — diversity in miniature Forest, Rift Valley wall, lake, flamingos, tree-climbing lions (occasionally). Compact and varied. Best for a half-day stop.
If you have to choose Pick Tarangire if you'll be there in dry season (Jun-Oct). The elephant herds are spectacular and the park has a much more wilderness feel.
Pick Manyara for half a day en route to Ngorongoro, especially if you're travelling with kids or in the green season.