I don't know about you guys but when I travel to another place, the last place I want to eat is at an American chain restaurant like Mcdonalds or KFC. Isn't trying the local food part of the experience of travelling to another culture? Try some local barbeque, some fresh fish dishes, red rice, etc.
If you do find yourself at McDonalds in Guam in the morning, try the "Portugese Sausage, Eggs, and Rice" or "Spam and Rice" they are both only available at Mcdonalds in Hawaii and Micronesia. Come to think of it, you can try red rice at KFC too. hehe.
I think Universal Diver meant, stay away from the places that target Japanese tourists, not the Japanese places. There are quite a few Japanese restaurants in Tumon worth checking out that also have good prices. Also Chinese, Vietnamese, etc. Aji Ichi used to be my favorite budget Japanese restaurant when they were in lower Tumon.
Another place for local breakfasts is Shirley's or Kings. They are both Denny's-esque type restaurants but both have some good local dishes. Shirley's has some fish dinners too for great prices. The Chamorro Village in Agana also has some good plate lunch budget eats. They have a food court there with some variety, they also have some shops there all selling stuff having to do with Chamorro culture that are not as touristy as the items you will find in Tumon. If you're craving raw fish after diving (I always do), check out the Fisherman's Co-op next door for cheap fresh sashimi cut up and ready to eat.
I agree, Guam Plaza is also another cheap hotel alternative. If you really want to budget and don't mind staying in a motel, their are several around Tamuning, upper Tumon, and Agana.