Preheat oven to 425 degrees. Place beets on parchment-lined foil; drizzle with 1 tablespoon oil and season with salt and pepper. Fold parchment and foil into a packet and tightly seal; roast until beets are tender, about 30 minutes. Carefully open packet and let cool. Remove skins from beets and cut into wedges.
Combine beets, watercress, radishes, avocado, and chives in a large bowl. Season with salt and pepper. Whisk together vinegar and remaining tablespoon oil and season with salt and pepper. Drizzle over salad, gently toss, and top with goat cheese.