Carrie L in comments had jokingly asked about Chick-fil-a...one of our favorite meeting places. But no...there's not one within several, several thousands of miles away. I think CA has the closest one.
On base we have the usual base outlets...Burger King, Robin Hood ( a Subway wanna be), Baskin-Robins (with 6 not 31 flavors), a real Subway, and Anthony's (Very Nasty) Pizza...and for some strange reason Anthony's also sells fried chicken and rice dishes. We also have two short order grills - one at the bowling alley and one at the golf course both of which were good when we went. (One lady from the office did get sick after eating at the golf course...you really should stay away from anything made from mayo there.)
We also have a club (it's consolidated - office and enlisted together -AF wide they couldn't make money running two clubs so most bases are combined). Last night we went to fajita night - I think is was very good...Drew said it was okay. It was the first Mexican we had had other than what we've done at the house. There are several Mexican restaurants on island, but we have yet to get there when they are open.
Off base there is just about all the fast food chains except (Chick-fil-a) as well as some of the bigger serving restaurants. We have Lone Star, Tony Roma's Ribs, Outback, TGIF's...I'm sure there's more... Rumour has it that we'll get an Olive Garden and Ruby Tuesdays. Within the next five years 8,000 marines will open a new base here (relocating from Japan) so I'm sure several more chains will come in then. We've been to a few locally own places which we enjoyed. My favorite is Jamaican Grill.
The most important thing to remember when eating at a restaurant in Guam is to make sure there's a big "A" on the door. That means they have passed the health inspection. There could also be a "B" or a "C". And I'm told they are voluntary. I'm not sure what they have to do or not do to get a grade, but I think it just down-right scary that you can open and run a restaurant and not have certain health standards - or any for that matter.