If you don't want to spend too much money, hostels are a good option. Prices start in 8 euros. You maybe think that they are very cheap and for this they are unconfortable, by you are wrong, they are very confortable and give you services. Here you have a link where you can see information about this.
Shehe Bungalows (Zanzibar)
Mount Livingstone Hotel (Mbeya)
http://www.twiga.ch/TZ/mtlivingstone.htm
Here you've got more links:
http://www.hostelsclub.com/city-ca-528-Zanzibar.html
http://www.spanish.hostelworld.com/Albergues/Zanzibar/Tanzania
http://www.shehebungalows.co.uk/
http://www.twiga.ch/TZ/mtlivingstone.htm