A little bit after we were married I overheard somebody mention Gator Jack's in Rigby. We stopped by after school one day- mid afternoon and were greeted by Jack himself, who let us sample a few different things before we finally decided on what we wanted, now it is a favorite place of ours. The sandwiches are delicious and totally loaded down (4 inch is their small size, and totally big enough for most people).
I like to stick with what I know I like so I usually order and Up Yonder! or Shine from Da Moon. You'll have to go in to find out what those are. My husband has tried most of them but his favorite is the Kissin' Kin. A fun thing is to get an order of gator bites- they are mini baked potatoes... so good!
Gator Jack's now has two locations- in Rigby on Farnsworth way, right off the highway and in Rexburg across from Porter Park.
(note- these pictures were taken from the Gator Jack's website. When we got some on Friday I realized after I finished my sandwich that I was supposed to have taken pictures.)
If you want something to do after you eat, Rigby Bowl is nearby.