As you would expect from a capital city, Tegucigalpa [1] offers a wealth of hotel rooms in all price ranges. Most visitors on a budget will want to stay in the downtown area, which is where many inexpensive and midrange hotels are located. More well-heeled travelers can choose from quality hotels in Colonia Palmira and out on Boulevard Juan Pablo II, southeast of downtown.
Comayagüela [2], across the Río Choluteca, also has plenty of hotels in the budget and midrange categories. While Comayagüela is not the safest or most interesting neighborhood, it could be an option for travelers arriving late or departing early by bus, since many bus companies have their depots here.
Links:
[1] http://www.moon.com/destinations/honduras/southern-honduras/tegucigalpa
[2] http://www.moon.com/destinations/honduras/southern-honduras/tegucigalpa/accommodations/comayaguela-accommodations