We just spent 1 month traveling around Tanzania.
None of the northern parks will even let you near the parks, Ngorongoro definately wont let you in, not even on the bypass road.
Our favorite park in Tanzania was Katavi, they will let you drive on the bypass road right through the middle of the park for no charge but to explore the park you have to be in a truck. This was truly the best park in tanzania as it has loads of animals on no tourists, we were there for two days and were the only tourists in the whole park, compared to the northern parks where you see a lion and 25 tourists looking at it.
We kept a journal on our website for more info
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Best of luck and enjoy.
We also found a park in Zambia that allowed us, Kafue National Park, we were able to carry a ranger with us but we had the option of going by ourselves.