I got to see a lot of the local culture and several historical sites and geographical wonders, but the history of the nation is a bit hard to find, and what I did hear or read there tended to be focused on either a specific cultural narrative or fairly unsourced.
John Iliffe's History of Tanzania is pretty good, coming from a veteran African Historian (he's British, but has been writing since the sixties, and specializes in Tanzania).
Also read up on the Maji-Maji Rebellion, and on the East Africa Campaign in WWI; those are two key events in Tanzania's history as a German colony.