Preheat grill to medium-high heat. Remove husk from corn on the cob and brush with olive oil. Toss the shrimp in oil. Season the corn and shrimp with salt and pepper.
Place shrimp in a grill basket, grilling mat or on a piece of tinfoil to grill. Place corn cobs directly on the grill. Grill shrimp for about 4 minutes tossing frequently. You will know the shrimp are finished when they are pink and curl into a C shape.
Grill corn for about 8 minutes rotating every 2 minutes. Close grill between rotations to evenly cook.
Remove the corn and shrimp from the grill. While the corn and shrimp are still warm, chop shrimp into bite size pieces and cut the corn off the cob and add them to a mixing bowl
Add the goat cheese, tomatoes, fresh basil, and vinegar to the mixing bowl and toss to combine. The slightly warm corn and shrimp should melt the goat cheese to make a perfect creamy grilled corn salad