Mara: The Fairmont Masai Mara is amazing. The price can vary a lot -- it could be $500-600 in high season, but there are occasional sales, the infamous friends and family rates, etc. The facilities, guides, and location are all perfect.

Nakuru: there are indeed lots of flamingos That's about the only thing, though, unique about it.

Amboseli: It has large numbers of elephants, which tend to stay in packs. Even though vehicles must stay on roads in Amboseli (unlike in the Masai Mara), you can get very close to herds and see all sorts of elephant behavior.

There are elephants in the Mara, of course, but there are many more of them in Amboseli (or many more than you can actually get close to, anyways).

The other thing to see in Amboseli is Kilimanjaro -- it's only a short distance away. At some times of year this can be hit or miss, with clouds blocking the view for days on end.

Those are the only two things unique about Amboseli. There weren't a ton of other animals when I was there.

It is unclear whether you have 3-4 days total for safari, or 3-4 for the Mara plus days elsewhere. If the former, it might be best to stay just in the Mara -- seeing the cats, kills, etc. can be hit or miss so it's prudent to give yourself 3 days or so there. (In my last drive in the Mara, we saw hyenas killing a gazelle, a lioness dragging a wildebeest towards another lioness, and otriches mating in 30 minutes. On other drives, not much. It's like a box of chocolates)

If you have 3-4 for the Mara plus time for a day or so at Nakuru or Amboseli, then it's worth it. The road between Nairobi and Amboseli is quite good. The road between Nakuru and the Masai Mara gets quite bad near the end.

If it doesn't eat into the time for seeing other things, if you were going to go north to Nakuru, you may also consider going up to Mount Kenya. The mountain is interesting, you're on the equator (signs everywhere), and there's the Fairmont Mount Kenya which is quite interesting.