OK, so Lisa H. asked me to post some good ideas for veggies on the grill. Perfect timing, because recently I went to Target's outdoor section, and they had all their grill stuff on clearance. So I bought a little metal basket-type thing with holes in it for grilling veggies... right up my alley! You don't HAVE to have this little contraption in order to grill veggies, but it's made it a lot easier for me. You can also form a low-lying rectangular box with edges out of foil and put it right on the grill. It's just a little more precarious.
Here's what I did: I just cut up all different-colored peppers, fresh mushrooms, yellow squash, pre-boiled red potatoes, and an onion (red or yellow), tossed them with some olive oil, kosher salt, and fresh-ground pepper, threw them in my little basket and put the basket on the grill next to my chicken. It's that easy! Just turn the veggies a couple times and cook them till they look right to you. You can also toss in some minced garlic and/or parmesan cheese, if that's more of what you're in the mood for. Just experiment and have fun!