Grill the first two slices of the watermelon, the tomato, the cucumber and jalapeno over high heat for about 5 to 6 minutes per side until you have good grill marks and a little seared. Adjust the heat to keep everything from burning. Remove from the heat.
Remove the rind from the two slices of watermelon and cut into chunks. Remove the skin from the tomato and jalapeno, cut the tomato, cucumber and jalapeno into pieces and place everything into a blender. Add the onion, the salt and pepper, and vinegar and blend until smooth. During the last minute, drizzle in the olive oil. Pour through a colander to capture any seeds and other small bits into a large bowl. Taste and add more salt and pepper if needed. Cover with plastic wrap and refrigerate until cold. This can be made the day before if desired.
Cut the remaining slice of watermelon into 8 wedges. Divide the gazpacho between your serving dishes. A martini or margarita glass makes for a nice presentation. Garnish the top of the gazpacho with the diced avocado, cucumber and onion. Using a squeeze bottle put a few drops of the balsamic vinegar in each serving. Cut a slit in the pointed end of the watermelon and slip one segment of watermelon wedge over the edge of each glass. Serve cold.