What would be the Unicode character for big bullet in the middle of the character?

http://www.unicode.org is the place to look for symbol names.

● BLACK CIRCLE        25CF
⚫ MEDIUM BLACK CIRCLE 26AB
⬤ BLACK LARGE CIRCLE  2B24

or even:

🌑 NEW MOON SYMBOL   1F311

Good luck finding a font that supports them all. Only one shows up in Windows 7 with Chrome.