'For' used in this sense means 'on behalf of someone' or 'for someone's benefit'. If your mother does your laundry for you, she does this on your behalf. If you do something 'for yourself' it means that you don't engage another person to do this for you. In this situation, he didn't want anyone else to help him find his way - he wanted the discovery of the city to be his own achievement. 'Nobody told me the secret. I just worked it out for myself.' 'By myself' would simply mean 'alone'. 'For myself' suggests that I wanted or needed to work this out, and that I benefited from having worked it out.

"He had to discover it by himself." "He had to discover it for himself." The usage of "by himself" and "for himself" are very similar. However, when you do something "by yourself", it generally means you do it "alone" without any help. On the other hand, when you do something "for yourself", it means that you want to do it "for your own sake", in a way so that you accomplish something or get some additional benefit out of doing it. He went to the library so that he could study by himself. (Alone, without any distractions, maybe so he could get his homework done faster.) He went to the library to study for himself. (Maybe he especially wanted to do some research in some field he is very interested in.) "By" and "for" in this usage have really subtle differences. I hope this helps.