Trim stems from beets to 1 inch; cut into quarters. Cut bell peppers into 1-inch-wide strips. Cut off ends of zucchini and eggplant; cut each lengthwise into 4 slices. Cut eggplant slices lengthwise into 1 1/2-inch strips. Cut onion into 3/4-inch-thick rounds.
Whisk together olive oil and vinegar in a large bowl. Add vegetables, and sprinkle evenly with salt and pepper; toss to coat.
Grill vegetables, covered with grill lid, over medium-high heat (350° to 400°). Grill beets 6 minutes on each side (we grilled on 3 sides) or until tender; grill onion, zucchini, eggplant, and bell peppers 4 to 6 minutes on each side or until crisp-tender. Cool beets slightly, and, if desired, peel.