Bus from Arusha is 4-6 hours, TSh11,000/=. Bus from Singida is 2 hours, TSh7,000/=.
Katesh is a small town and everywhere is within walkable distance.
Mount Hanang is one of the highest mountains in the country at just under 12,000 feet. The mountain is its own national park, which has luckily avoided the rampant deforestation present in other areas of Tanzania. As Katesh is a fair distance from the Serengeti-Arusha-Kilimanjaro tourism circuit, Mount Hanang isn't frequented by many tourists, meaning you will have the mount all to yourself. The climb begins in dense forest, which becomes thinner and more alpine as the altitude increases. A large variety of birds inhabit the mountain - house martens and other migratory birds winter on the summit, and hawks enjoy hunting in the thermals above the slopes. A permit is required for the climb. As of 2018 the fee was 12 USD, payable at the bank in Katesh where you will receive a receipt, which will then need to be taken to the tourism office. This process may take a day or two, and is impossible on Sundays. That being said, it is possible to avoid this process if you are attempting the mountain by yourself, as the mountain is rarely policed. A guide is recommended, though it is certainly possible to manage without one. If you would like a guide but haven't organised one prior, it's very easy to find a local in the town - just mention your plans to someone and a guide will materialise! Most have a good level of English. From the Katesh side, there is one way in, through a gate where you may be expected to pay the TSh 2,500 park fee. There is only one way up, and the path is well worn, making it easily navigable if you don't opt for a guide. The climb itself will take between 7 and 10 hours depending on your level of fitness. The high altitude is also likely to slow you down.
NMB is the only bank in town and has a cash machine. However, it does not offer access bank networks (Visa, MasterCard, etc.) - Arusha and Singida are the closest towns with this service.
Bus to Arusha is 6-10 hours, TSh11,000/=. Direct bus leaves at 6am; others originate in Singida. Bus to Singida is 2 hours, TSh7,000/=, originates in Arusha. Through buses will probably not have seats (you will have to stand).