I am gluten free and vegan. I usually eat fruit or nuts as my snacks. No beans makes things a lot harder. Have you tried quinoa? Even though they stick it in with grains, it is technically not a grain. It is the seed of a plant related to spinach. A lot of people who have problems with other grains do well on quinoa. And it is a complete protein, so it might work well for you since you don't eat beans. I make a porridge with it for the morning with some cocoa powder and almond milk and sweetened with stevia, it is really good! Or sometimes I make it with apples, cinnamon, and a sprinkling of walnuts.
chocolatecoveredkatie.com has amazing recipes if you love chocolate and want something healthy-ish (although some are quite high in calories). Oh and sweet potato fries are amazing! You could also do raw veggies (carrots, celery, etc) plain or with guacamole. Someone else mentioned apple and peanut butter, so yummy, or you could use almond butter if you are avoiding peanuts (bean family). Also I have discovered tons of amazing recipes on pinterest, so you might want to check there.