Line a baking sheet with foil. Preheat the oven to 450 degrees F.
Whisk the vinegar, shallots, and honey in a medium bowl to blend. Gradually whisk in the oil. Season the vinaigrette, to taste, with salt and pepper. Toss the beets in a small bowl with enough dressing to coat. Place the beets on the prepared baking sheet and roast until the beets are slightly caramelized, stirring occasionally, about 12 minutes. Set aside and cool.
Toss the arugula, walnuts, and cranberries in a large bowl with enough vinaigrette to coat. Season the salad, to taste, with salt and pepper. Mound the salad atop 4 plates. Arrange the beets around the salad. Sprinkle with the avocado and goat cheese, and serve.