The two more cinderblock looking lodges are the Kachina and Thunderbird Lodges which are essentially more "Modern" than the El Tovar and Bright Angel Lodges. Modern in the sense that they were built in the 50s-60s and have elevators to get to there upper floors (El tovar requires hoofing it up the stairs to get to your rooms). Check-in for Kachina is shared with the El Tovar and Thunderbird shares check in with the Bright Angel Lodge.
The El tovar is a really nice hotel, and the room are unique in the fact that some have an odd layout due to the architecture of the hotel. There wasn't any air conditioning last time I checked, but here in the dry, high elevation northern Arizona it never gets too warm along the rim of the grand canyon (the rim only hit above 90 about three days this summer, heck I don't have airconditioning here in Flagstaff, never needed it all summer long). Reservations can be very difficult to get as it is considered the flagship hotel of the park. Your other options on the rim are Kachina, Thunderbird (the two cinderblocks as a previous poster put), and Bright Angel Lodge. The Maswik and Yavapai Lodges are located away from the rim, but are all connected by the village shuttle bus (though the last two can be hard to get sometimes as they are used for Grand Canyon Railway passengers spending the night at the canyon through railway packages). All hotels at Grand Canyon are run by the Xanterra Corporation. Hope this helps