If you plan on being near the Gateway, it's only a 10 minute walk to the furthest of the EP area resorts. You can also take a Friendship boat, but walking will be faster.
Picabu at Dolphin comes to mind for your budget restraints, but it's pretty "no frills - other than decent food for the price." No ambiance to speak of. It's a cafeteria. Reminds me of a hospital cafeteria, really. That's not to say I don't like it, just need to keep your expectations in check on what it is.
Fuel, also at Dolphin, has killer sandwiches right around 10 bux (maybe more like 9.) They are worth every penny - I am cheap, but I will always pay for good food. That place is a true hidden gem (a recurring theme at Swolphin restaurants.)
Fuel is bright and airy (tho small.) It has a few long tall tables for eating in, and if they still have the self serv froyo, station, you could stretch that 10/per a bit, if you don't t go crazy and get a small froyo treat as well - at all of the "by the oz" froyo places, it can add up quickly.
Just keep the Ep area resorts in mind. They are just outside of the International Gateway.