Local buses cruise along the main streets through town for nfa2 per ride from roughly 6am to 9pm. Hop on at the back, where you'll pay the ticket taker.
The regional bus stand in front of Enda Mariam Cathedral connects the city to outlying villages, mostly notably bus 18 for Emba Derho in the first foothills on the road to Keren.
Given the popularity of bicycling in Eritrea and the compact nature of Asmara, it's surprising that there aren't more hire shops for visitors.
Dahlak Bicycles On the south side of town.
Share taxis carry passengers for nfa5 to nfa10 within the limits of Asmara, while contract taxis charge upwards of nfa50. Always negotiate a price before the ride.