I always thought that of Boston, Brooklyn, NY and even the Lakers, Boston would have offered Kyrie the best chance to win now, in terms of assets both that we have and that we could get. Even if he teamed up with KD at the Nets or Knicks, would they still be a better team than Boston with him, AD, Hayward, Brown, Horford etc? I couldn't see them being better, I just don't think they have the personnel outside their Big 2 (both of whom have had their share of injuries over the years). If you look at things dispassionately I think the Celtics come out the logical team that offers the best chance to win now.
BUT...the two factors not associated to competitiveness I always thought might sway the decision would be a) how accepted he feels with the Celtics and the fans; and b) his chemistry with Brad Stevens and Brad's style of play.
Earlier in the season and through most of last season he was relatively well-received by the fans, and he said all the right things about wanting to be here, wanting to get his number retired, about the team's history, etc. But as the season deteriorated the fan perception of him just became more and more negative to the point where for most people his playoff flameout was unforgivable and he was the root cause of everything wrong with the team (certainly he bears his share of the blame as the leader but I don't think it's all his fault). Kyrie says he doesn't do social media but I think even he would find it hard not to feel all the hate and anger from the fanbase. Who wants to play for fans who hate you anyway?
The other thing is whether he feels that Brad's schemes and playing philosophy will get the best out of him. The team can move asset pieces around to build him the team he wants but if he feels there's incompatibility of lack of chemistry between him and Brad then it would make sense for him to move somewhere else where the style of play is more suitable to his skill set.