Regardless of the time of day you decide to fly, the ticket price will remain around the same. Book flights from Illinois to Tegucigalpa as you normally would.
In terms of precipitation, rainfall in Tegucigalpa ranges from 0.0 - 7.1 inches per month. September is typically the wettest month, when rainfall can reach 7.1 in. January is typically the driest time to visit Tegucigalpa when rainfall is around 0.0 in.
If weather is an important factor for your trip to Tegucigalpa, use this chart to help with planning. For those seeking warmer temperatures, May is the ideal time of year to visit, when temperatures reach an average of 75.2 F. Travelers looking to avoid the cold should look outside of January, when temperatures are typically at their lowest (around 68.0 F).