I took my boys 18 and 21 on safari to Tanzania plus a week in Zanzibar and mostly we really loved it.
We did it on a budget so camped - although it was more glamping than camping. We did pay extra to have our own private safari guide which meant it was just the three of us in the jeep when on safari. It only cost a small amount more than a shared jeep and was totally worth it.
As pp said Ngorongoro was just breathtaking - there were a lot of other jeeps there but it is so vast that a lot of the time we were alone. The drivers radio each other if say someone spots a lioness hunting so if something special is happening often you will get 3 or 4 vehicles near to each other but the rest of the time you can usually only see the other vehicles in the distance.
We did five nights on safari and that was about right for us. I think on the last day we were about ready for a bit of R and R after being bounced around in the jeep for five days. Highlights of the safari were a night at Maramboi tented camp where the wild animals literally roamed around the tents and two nights at Naona Moru in the Serengeti, again with animals wandering in and out of camp. These parts were magical and something none of us will ever forget.
Our safari guide had teens of his own and was excellent at holding the boys attention so that helped but to be honest there were so many new and different experiences each day that there really wasn't time for them to get bored. One tip - I took a power pack with me so that we could keep our phones charged up and actually wi-fi was available more than you would have thought so the boys were able to send photos to their dad and friends pretty regularly.
I loved the week in Zanzibar, although we did very little except relax and chill out. We did a couple of day trips but to be honest it was lovely just to kick back and relax after the excitement of the safari. The boys were starting to get restless after about 5 nights though so a week was probably slightly too long for them.
Overall we all loved the safari and would do it again in a heartbeat. In retrospect I would probably have had a slightly shorter time in Zanzibar for the boys, but I could happily have stayed for another week of relaxation/spa/swimming etc...!
If it helps I used a company called Safari and Beach to design the holiday and they were really fabulous. I started with one of their standard itineraries but then customised it to add some parks and leave others. They also have an agent in Tanzania who is on hand if anything goes wrong which I found really reassuring as a woman travelling alone with her sons (albeit adult sons!) in a country I am unfamiliar with.