The most popular places on lake Itza to swim are San Andrés and it's neighbor San José. Right in between those two cities is the Hotel Bahai Taitza. It is a wonderful location owned and run by Mauricio. He attended english schools in Guate, and actually speaks better english than any other Guatemalan born Guatemalan I've met.
Mauricio cooks the best food anywhere and will let you swim and use his kayaks or hammocks at no charge. His rooms are well decorated, however have no air conditioning. Being so close to the lake with the cool breeze at night, a ceiling fan is all you really need on most nights. If that's a big issue for you, come during the cold months of November-January. The lake is still warm during that time, even though temperatures dip down into the frigid low 70s.
With a little advanced notice he can cater for big groups. This is also where Los Tigres stayed when playing a concert in Petén, as well as the Rojos (soccer team) when they come to play. He also makes a big Gringo Thanksgiving spread and lots of turkey for Christmas as well.