Roman Catholic Cathedral of Asmara is just one of the landmarks located 1 mi (1.5 km) from central Asmara, so you might want to stop by for a few pics during your trip.
National Museum of Eritrea is 0.4 mi (0.7 km) from central Asmara, why not stop by during your stay. If you want to experience more of the culture Asmara has to offer, head to Bell Tower, Cicero Stadium, and Bowling Alley.