From the word itself, it seem that好友 is closer than 朋友
in my opinion, people don't often refer to friend as好友 when introducing their friends, they say things like:he/she is my 朋友 or some times 好朋友 instead of 好友. The word 好友itself sounds a little bit cold and aloof because it's more commonly used in the internet word. For example: in xxx social networking site, xxx add you as 好友。The term 好朋友 is somewhat childish because we don't often see see adult referring other as their 好朋友。挚友is a more mature term for very good friend that you know for a long time, it is used in written form instead of in daily conversation. But being called 挚友gives people a harm-warming feeling. (I don't feel the warmth if someone call me 好友 in daily conversation, it's a bit weird to talk like that,好朋友 sounds way better/normal)
Normally, what people would do is to to add adjectives before 朋友 。such as 我高中的朋友(my high school friend), 很要好的朋友(very close friend colloquial),很亲密的朋友(very close friend less colloquial)