Is a Gemini and a Virgo a good best friend relationship?

Best friends are not Astrological placements.~ They are heart,and just who makes them tick.~*

Mercury in Gemini (dignity): As Venus is the soul-centered ruler of Gemini, this position combines the influence of this planet with that of Mercury. The net result gives the individual the potential to fuse and relate many streams of diverse thought into a vision and expression of harmonious unity. On the personality level,
Mercury in Gemini bestows the ability to access and amass an abundance of knowledge and information that may then be stored or distributed. The life objective is to cultivate pure reason and objective powers of analysis.

Mercury in Virgo (exaltation): What is taken apart through analysis in Gemini is put back together on a higher level of understanding in Virgo. It is in this sign that one learns discrimination in form. This can be the form of an object but it can also be the form of a thought. It is in Virgo that we come to achieve a more perfected way of communicating as the soul-centered individual realizes that Divinity is also contained within mind. In essence, ideas here gestate until they are ready to come forth with healing potential.

If both keep that difference in mind...it just might work out.

Leo sun/mercury

No. Geminis don't have time for critical negative complainers. They're too brezzy. Virgos are fascinated by Gemini intelligence but that's all to it.