There are two choices...either Asuna or Eugeo. Who had the strongest connection with Kirito? Remember, Asuna and Kirito got to know each other very well in Aincrad as well as spending a year and a half with together in the real world. However, also keep in mind that Eugeo was with Kirito throughout the course of two years, so he deffinitely got to know Kirito pretty well too. I do NOT count the 10 childhood years Kirito spent with Eugeo as Kirito does not remember them. After reading all the way through to chapter 16 so far, I can see why everybody was saying that he was a very good friend to Kirito.
So take your pick...who is Kirito's best friend? Is it Asuna or Eugeo?
Edit: Now that the movie has come out, I think that should deffinitely be thrown into the mix that is Kirito and Asuna's bond!