Arusha is the safari hub for Tanzania's "Northern Circuit." The city itself has a few interesting sights (notably the Arusha Market), though it's mainly used by safariers overnighting from their international flights before moving on to their safaris in the Serengeti, Ngorongoro Crater, etc.
Arusha National Park, the closest national park to the city, is highly underrated and easily accessed via Arusha. Though one of several national parks/reserves comprising the “Northern Circuit,” Arusha National Park is distinguished by its predominantly forest-inhabiting animal populations. However, it’s not exclusively a forested landscape. In fact, the park is an ecological kaleidoscope, composed of highland rainforest, acacia woodlands, crater lakes, and open grassland. Blue Monkeys, black-and-white colobus monkeys, bushbuck are prevalent in the highland rainforest, while red duikers are occasionally seen. Burchell’s Zebra and other big game inhabit the open grasslands.
The park is also very photogenic: both Mt. Kilimanjaro and Mt. Meru may feature as a backdrop for any number of your photographs. Mt. Kilimanjaro is best seen in the early morning, as cloud coverage tends to obscure the view thereafter. Mt. Kenya is located within the park. Summiting require rock climbing experience and armed guards. Alternatively, there are a litany of hiking trails leading to rivers and waterfalls.