There is at least a potential conflict of interest when a Judge is "best of friends" with one of two or more lawyers appearing on a legal matter before that Judge. Though not lightly invoked, if you believed their relationship was so close that it could effect the impartiality of the Court, you could ask the Judge to recuse himself/herself. However, you will likely offend not only that Judge but the Judge down the hall, so you should have some evidence to support your position and not just speculation.
Lawyers often know and/or a friends with a litigant in their court. That alone does not create a conflict. As for "best friends" that would be a very fact specific matter. Have you raised the issue with the Court on the record? Have you asked the Judge to recuse himself?
I am a former federal and State prosecutor and now handle criminal defense and personal injury/civil rights cases. Feel free to check out my web site and contact me at (212) 577-9797 or via email at Eric@RothsteinLawNY.com. I was named to the Super Lawyers list as one of the top attorneys in New York for 2012. No more than 5 percent of the lawyers in the state are selected by Super Lawyers. The above answer is for informational purposes only and not meant as legal advice.