I feed snow peas as for the celery I cut it up as the long veins in the celery and choke the rabbits.
Grass, apples (without core and seeds), basil, alfalfa, radish, clover, beet greens, broccoli (leaves and stems), brussel sprouts, carrots (treat only), celery, chicory, cilantro, dandelions, dill, tops of dutch carrots, endive, parsley, pea pods, cos lettuce, spinach, watercress, wheatgrass, unlimited amounts of hay.
Wild rabbits eat mainly grass. So letting your rabbit out into the backyard to nibble grass is a great idea.