Tanzanian food is more interesting than its reputation suggests. The mainland has a few staples that appear everywhere; the coast and Zanzibar have something considerably more exciting.
Ugali is the national staple — a stiff white porridge made from maize flour, served alongside meat stews, beans, or greens. It's eaten with the hands, shaped into a small ball to scoop up the sauce. Plain on its own, but the key is what it's served with.
Nyama choma (roasted meat) is widely available and worth seeking out at local places where it's done right over charcoal. Usually goat or beef. Order it with kachumbari, a fresh tomato and onion salad, and a cold Kilimanjaro beer.
Chipsi mayai — chips omelette — is the most beloved street food on the mainland. French fries folded into beaten egg and fried into a flat omelette. Found everywhere, costs almost nothing, and surprisingly satisfying.
Wali wa nazi (rice cooked in coconut milk) is the gateway to the coastal style of cooking, where Arab, Indian, and Swahili influences come together. On the coast and in Zanzibar, the food becomes distinctly more fragrant and spiced — cloves, cinnamon, cumin, cardamom — a product of centuries of trade.
Zanzibar pizza is actually a folded street pancake filled with eggs, vegetables, and meat, fried on a griddle. Nothing like Italian pizza, and much better than the name implies. Find them at Forodhani Gardens in Stone Town in the evenings.
Maandazi are lightly sweetened fried dough triangles, eaten for breakfast with very sweet tea (chai). They're ubiquitous and good.
For drinks, Kilimanjaro and Safari are the main local lagers. Fresh sugarcane juice and passion fruit juice are excellent where available. Coffee is grown in the highlands around Kilimanjaro and Mbeya, though finding a good cup of it actually served in Tanzania requires some hunting — most export-quality coffee leaves the country.
Vegetarians are reasonably well served in towns, where bean stews, lentils, and vegetable curries are common. In remote areas, options narrow to ugali and greens.