I find this Danish recipe for pickled beets to be not too vinegary:
Scrub your beets. Leave ~1 inch of the stem. Do not cut off the tip. This is to prevent leakage of the juices. Put the beets in a pot with lots of cold water. Boil the beets for 1/2 to 1 hour, depending on the size of the beets. When they are cooked, plunge the beets into cold water. When the beets are cold enough to handle, rub off the skin. Slice into nice slices.
Put the slices in a clean jar or crock and pour the boiling pickling liquid onto the beets. If you like, include some whole cloves or slices of horseradish.
Pickling liquid for each kg (2.2 lbs) of beets:
Boil 4 dl vinegar, 2 dl water and 100-125 grams of sugar.
4 dl = 1.69070114 US cups
100 grams sugar ~= 1/2 cup
I use cider vinegar.