How clean & how big?
Forstner bits work well, but to get them smaller than 5/8" or so you need to go to Fleabay.
Brad-point bits work OK, but they tend to like harder wood -- contest balsa may not be the best for 'em.
I've had good but mixed success with making "sorta Forstners" out of regular twist drill bits -- basically I grind them hollow, so that the edge of the bit is slicing through the balsa. You need good bearings on your drill press, though -- without the Forstner's centering brad they really want to wander. And they don't self-clean the hole at all -- you need to peck, then blow them off, then peck, then blow, maybe going 1/32 of an inch each time.
None of these make a hole that's knife-edge straight on the backside, but all of them do way better than twist drills. The Forstner bits do best, and the sorta-Forstners come in second when they're sharp and I'm not impatient.
Here's a picture showing what I mean, with a 3/16" sorta-Forstner and the back sides of two holes that I drilled with it. The one that's a bit torn up is the one that I did first, and re-learned the meaning of "slow enough" -- I got impatient on the last peck and went too far. The bit could use sharpening, too -- from all accounts balsa is incredibly abrasive for being as soft as it is, and I certainly know that I need to sharpen my tools a lot when I'm not just using disposable blades.