Its true there hapen things in Tegucigalpa, but many depends on yourself of course. I would say don't show around with you digital camera in fonrt of the many streetchildren and don't just walk around after dark.
Comayagüela, Tegucigalpa's twin city, might even be more dangerous.
If you do stay here you can visit the many churches around. In the inner city at the 'plaza de morazán' you'll find the cathedral, a little further 'San Fransisco', ....
Another interesting place can be the museum 'Museo de la historia Republicana Villa Roy' where you can see as well old mayan sculptures as modern Honduran art.
Favorite thing: Tegucigalpa is the capital of the country, but many tourists avoid this area. Because of insavety and just because there's not much to see. I stayed here lets say about a week and I have to say they're wright! There is almost nothing to see, it's a very dirty city and well about savety...I think its still saver than for example San Pedro Sula, but also here you have to be carefull.
go to Yoland's Spa- it's wonderful. My favorite resturant is the El Patio. They have built a new building, on a different site, and it is very modern. They have patio area with an open grill. It smells great as soon as you arrive.
Fondest memory: The Mission house where we stay is on a hill above the city. At night I can lay in my bunk and see the lights of the city below.