When you’re ready to get out of Tegucigalpa, find highway N-25 at the northeastern part of the city near the Modesto Rodas neighborhood. Take this all the way to Talanga some meandering 60 km to the north. Good points to stop for the view or to take in the local scenery include: Santa Lucia, Valle de Ángeles, San Juancito, and San Juan de Flores. Somewhere north of San Juan de Flores, the tarmac ends and a wide, unpaved-but-well-graded highway takes you the rest of the mostly straight way to Talanga.
From Talanga, either complete a circuit back to the capitol on the Carretera a Olancho or perhaps continue north on the N-43 passing through El Porvenir (“The Future”) on your way to El Progreso (“The Progress”) and the Caribbean Sea just beyond. When I did it I had already visited the Caribbean so I actually continued on the Olancho Hwy as far as Catacamas in the northeast. It was a pretty and pretty solitary ride.