If you are in Asmara for a short stay, the best thing to do after you're done sightseeing in this city is to head for the outskirts where the scenery is stunning at the very least.
Unless you come from a high altitude area yourself, you need a couple of days of strolling in Asmara to get your body used to the thin dry air at 2,600 m 8,530 ft.
Bring lots of sunscreen lotion but also a sweater as it can get really chilly not only at night but even when standing in the shade temperatures can vary greatly on different sides of the same street depending on the position of the sun. The sun shines very bright throughout the day in Africa, especially so in Asmara where clouds are rare, so unless you enjoy squinting, bring UV blocking shades.
If you like hiking, rock climbing and mountainbiking, the above mentioned areas outside of town are excellent places to do so, but bring your own gear incuding bike as there are no rental bikes and a very limited supply of safety equipment shoes, ropes, etc. in Asmara. However, tents and mosquito nets are readily available at an affordable price in the marketplace downtown. Also consult the locals and bring a guide, because it is good to have someone familiar with the place who speaks the local language in case of an accident or any other eventuality like what is legal and not legal. For example, taking pictures around any government installation or authority police, airport, ministries etc. is strictly forbidden, and your guide can help you get out of such sticky situations.
Finally, take time to savor some good food in Asmara. Don't drink any "fresh" fruit juices or eat any ice cream unless you want health issues to mess up your time. Stick to bottled drinks, unpeeled fruits and cooked food.
