I break out the grill several times a week during the summer, and veggies on the grill are one of my favorites. I love having zucchini, yellow squash, onion and mushrooms--but use whatever you've got.
After you've cut the veggies into similar size pieces, I like to toss them in a ziplock bag or bowl with some balsamic vinegar and oil (or just use Italian salad dressing) for 15 minutes while the grill is heating up.
I use a grill basket to keep things all contained (pick one up at TJ Maxx or Ross). I heat the grill up to med-high and keep the lid closed most of the time with occasional stirring.