My favorite substitute would be celeraic (celery root)

If your salad uses beets for their pop of color as well as their flavor, carrots come in some of the same colors--purple, magenta, red, yellow--and their flavor isn't as earthy as that of beets. Check a farmer's market or a neighbor's garden--rainbow carrots aren't usually carried by chain groceries.

The purple ones are best served raw--the color fades to an unappetizing shade when boiled or when dressed with anything that's acid-based. (I once garnished a bowl of cole slaw with curls of purple carrots, which turned the dressing a shade of magenta more suitable for a beautiful sweater than for anything edible.)

Or try the recipe with baby golden beets, which are much sweeter, less earthy and less messy than regular beets

roasted sweet potatoes

Are the beets roasted? If so, how about roasted apples?