One of the easiest and most cost effective ways of eating while traveling is to hit the local grocery store. If you've decided to rent an apartment, you can cook your own meals with relative ease. If you at least have a fridge in your hotel room, you can store your snacks for when you need them. You get the added bonus of eating like a local.
Jenni and I had a great time in Bermuda, but the food was pretty pricey, and for us a little difficult to find. While we were walking around downtown Hamilton we found a great grocery store right next to where the cruise ships dock. It was a really hopping place, and the selection was great and the staff super helpful. We ended up with 5 bags of groceries for about the price of dinner in our hotel.