Baulk generally means to stop and refuse to go on. Avoid implies that you keep away from the challenge, usually by an alternative means. Say you're walking and you run into a really big wall. To baulk the obstacle would be to stop, refuse to continue, and go back. To avoid the wall would be to somehow go around the wall without dealing with it. In your example, to baulk the costs means that the parents stopped when they saw the costs and refused to buy from those dealers. That is why they had to continue looking. If the parents avoided the costs, that means that they got a cello without paying the high costs (maybe they knew someone who gave them a discount).

baulk is BrE balk is AmE. It means 1. to not want to do or try something, because it seems difficult, unpleasant, or frightening 2. formal to stop someone or something from getting or achieving what they want avoid means to prevent something bad from happening. from: Longman They are not the same, but quite close in meaning. You'd better ask a nativ speaker, because I'm not sure.

In this sentence 'baulked' means 'shocked at the price and didn't want to pay it'