Jeff,
Although darkness is a special effect used by several attractions at the Magic Kingdom (hence the term "dark rides"), there are numerous attractions that do not have any darkness.
To make sure you avoid the appropriate attractions, I'll list the
dark/darkish attractions to avoid...
Main Street USA: None
Adventureland: Enchanted Tiki Room, and Pirates of the Caribbean
Frontierland: Splash Mountain, Thunder Mountain Railroad (brief darkish moments), and Tom Sawyer Island (only the cave are dark - the rest should be fine)
Liberty Square: Haunted Mansion
Fantasyland: Peter Pan, Snow White's Scary Adventure, and Winnie the Pooh
Tomorrowland: Space Mountain, Stitch's Great Escape
If you have any further doubts, a good way to preview attractions for any possible issues is to search for them on www.youtube.com. Most attractions have multiple videos posted on YouTube, so you can get a fairly good idea about the attraction in advance (may spoil the fun a little for you, but you're willing to "take one for the team" - right?!)
Please write again if you have further questions.