The places you just can't miss
The United Nations National Park on El Picacho Hill just north above the city offers a great view of the city and hosts the Picacho Metropolitan Zoo. The park is a regular place for locals to visit and picnic on the weekend. It has a huge statue of Christ that can be seen from anywhere in the City, a zoo (It is really not taken care of, I wouldn't bother), a replica of the Mayan Ruins, a little botanical park and a sort of zen-like park with a Confucius statue.
It really is worth going, the view is fab, the picture of Christ over the city is a must, plus the walk around the mini botanical, zen, Mayan park is nice. It gets chilly.
I think there is a fee, a small one. I'll get you the info as soon as I can.
According to Wikipedia, there are 14 museums in Tegus. The ones I recommend are all located in downtown Tegus, in the historic part.
Here are the ones I can remember.
National Identity Museum (Museo para la Identidad Nacional)
This one is my personal favorite.
You can visit their webpage at http://www.min.hn/ or look for them on facebook Museo Para la Identidad Nacional .
National Anthropology and History Museum or Villa Roy National Museum (Museo Nacional de Antropología e Historia-Museo Nacional Villa Roy)
I found this blog about it http://museovillaroytgu.blogspot.com/
National Art Gallery (Galería de Arte Nacional)
Has 6 permanent art exhibits and is located right beside the National Congress builduing downtown. Visit their facebook page:
Republic History Museum (Museo Histórico de la República)
Museum of Man (Museo del Hombre)
Telecommuncations Museum (Museo de las Comunicaciones)
Military History Museum (Museo Histórico Militar)
Archaeological Museum (Museo Arqueológico).
The Natural History Museum (Museo de la Historia Natural) - is located within the National Autonomous University of Honduras.
Numismatic Museum (Museo Nimismático Rigoberto Rojas) is located in Comayagüela next to the Central Bank of Honduras Annex building.
Centro Interactivo de Enseñanza CHIMINIKE)
Other than the museums, downtown Tegus is full of little places even locals don't bother to visit and truly add a magic to the place. The neat thing about Downtown is that everything is near and within walking distance, you could visit all these places in a day, even half a day.
The Cathedral of San Miguel Arcangel
Los Dolores Church (My favorite)
San Francisco Church
La Merced Church
La Leona Park
La Concordia Park
Palacio de Comunicaciones
El Correo Nacional
Teatro Manuel Bonilla
Antigua Casa Presidencial
Valle de Angeles
A Soccer Match