In the Mountains of the Moon: The Usambara and Kilimanjaro by Jens Finke is a useful regional guide covering the natural history and hiking routes of the Eastern Arc Mountains including the Usambaras.
The Scramble for Africa by Thomas Pakenham (1991). A comprehensive history of the European partition of Africa, covering the German colonial period in what became Tanganyika — including the establishment of the hill stations and agricultural research stations in places like Lushoto (then Wilhelmstal). The chapter on German East Africa gives essential context for the colonial architecture you see in the towns.
Fields of Fire: An Atlas of Ethnic Conflict edited by Robin Poulton — less directly relevant, but for understanding the complexity of Tanzanian political history since independence, this gives useful background on the country's relative stability compared to its neighbours.