Changing money in Tanzania is not a problem in most populated areas. Hotels usually have a worse rate than banks, so you should go to the bank. You may have to wait in line for a bit. Banks in Tanzania are just like banks in the US. Main branches include NBC and Standard Chartered.

ATMs are in most all banks with 24-hour access and give the same exchange rate as the bank. They may require a Visa card. Inquire if there is any additional fee for withdrawing using a Visa debit card.

When leaving the country, if you need to exchange money back for USD, the Forex has the best Tsh to USD rate. There is a Forex in Moshi, but check into other areas.