Root Crops such as Beets can be planted now for an early summer harvest. Suggested varieties Early Wonder or Detroit Dark Red
Carrots planted in April will yield an early summer crop. Suggested varieties - Little Fingers or Paris Market.
Onions - April is the best time to get Onions started from seed in most regions. Select a variety appropriate for your region. Cooler climates should be planting long day onions. Warmer regions should plant short day varieties. See - Onion Varieties
Potatoes - April is a good time to set out potato slips - as always check for the correct variety for your gardening zone. See - Potato Varieties
Other Root Crops that can be started in April include
Radishes can be planted from seed in early spring and will be one of the first crops you harvest
Horseradish is a perennial that can be planted now, you may want to select a corner of your garden that receives little traffic. A common problem faced with horseradish is keeping it from growing where it's not wanted, it can easily invade areas delegated for other crops.