Hike the Lion Rock also called Simba Hill in the north of the city to have a nice view of the surrounding. However, do it in a group of at least 4 people as there have been reports of muggings.
Excursions
On request, Dodoma Travel Cafe offers Trekking and Excursions.
Swimming Pool
There are two places with a swimming pool: The New Dodoma Hotel, 4.000 TSH for non-guests, and Climax Club, near the prison, where you can buy food, watch TV, and spend the day.
Gym
The New Dodoma hotel also has a gym, 7-9 and 17-19, closed Sundays, 4.000 TSH for non-guests.