You have to fly into Guatemala City. It's a three hour drive or more from there with traffic.
MichiganZ's response is excellent. If this is yr first trip to Guatemala, you MUST read about travel there before you arrive (Lonely Planet, for example) to maximize yr safety and enjoyment. As tourists we are more secure than others in Guatemala, but it is still a high risk area for various forms of serious badness, especially in the city. Do NOT take chicken buses anywhere near Guatemala City. Arrange for a tourist shuttle -un colectivo- to leave from Guatemala City in the morning. Travel in the morning is key if you want to arrive at CDM the same eve - boats from Panajachel to CDM end around 7pm, but also the late afternoon waves on the lake can be an issue to avoid. You can use any of a number of travel agencies to book the colectivo - and you can of course ask for a private colectivo and pay more if you want.
I have not stayed in a room at Hotel Casa Del Mundo, but I ate lunch and it was excellent. I met the owners, a very nice couple who built the hotel. And I was given a most friendly tour of several rooms. All appeared comfortable and serviceable, as well as reasonably priced. The public boat from Panajachel to the hotel should run you about 20 each, one way; the lancha privadas around 150 Q each, but a lot less crowded.
Well, it's 6:30 AM here now, and it appears as if you already have the answer to your question. But, here goes: The principle Guatemala International Airport is code name GUA, for Guatemala City, Guatemala. There is another airport in the north, in El Petan, at Santa Elena, next to Flores on Lago de Petan Itza, but unless you are flying in from Belize City to visit Tikal, you likely want to arrive in Guatemala City, since for a first trip into the country, you likely want to head for Antigua ( 45 min. From Guatemala City, if traffic is light, one and one half hours if heavy ). From Antigua you can reach Lake Atitlan, Panjachel, in another 3 hours by bus, private car or shuttle. note: I do not recommend the "chicken" buses for such lo ger trips. Lake Atitlan is a likely second destination for a first time visitor. If Tikal is your objective, you can reach it by a 1 hour connecting flight from Guatemala City. There are only some few other airports ( many existing in name only ) for charter flignts.
Enjoy our stay in Guatemala, the best kept secret in Central America, although the "secret" is leaking out.
The airport is in Guatemala City. You drive 3 hours to Panajchel, then take a boat to the hotel. My advice would be spend the night in Pana or Guatemala City and then take a boat to the hotel the next day.
Get an answer from La Casa del Mundo Hotel staff and past guests.