Rock Lee, because of his 'never give up' attitude, and because a lot of people saw him as a failure because of his problems with chakra (something Naruto can relate to).

Well he married Hinata, but in terms of friendship I'd say Shikamaru. They seem to hang out regularly

Hinata obviously.

Luffy.

Hinata and shikamaru

Shikamaru and Rock Lee;

Shikamaru's role as advisor says a lot; plus, from the beginning of Naruto, Shikamaru was one of the most chill ninja towards Naruto which makes sense why he would be one of his most trusted advisors. Shikamaru comforted and consoled Naruto after Jiraiya's death, arguably the most sensitive point in his entire life, by comparing his situation to his and Asuma's. Shikamaru earned (wholeheartedly, in my opinion) the trust of Hokage Naruto.

Rock Lee, in my mind, is one of the most significant and under appreciated roles in Naruto's life. All of Naruto's perseverance and stick-to-it-ness comes from Rock Lee, it seems, as all of Naruto's "Never Give Up" seems to come after Lee's introduction.

It's also worthwhile to note, it seems, that Rock Lee actually beats two of Naruto's nemeses in the early anime/manga: Both Sasuke and Gaara. Lee is an incredible ninja, which of course Naruto respects, but unlike Sasuke and others he's known until that point, Lee is a genuine and compassionate human being which Naruto respects and obviously envelops into his own personality.