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.

Here's full list of black dotlikes from unicode

● - ● - Black Circle
⏺ - ⏺ - Black Circle for Record
⚫ - ⚫ - Medium Black Circle
⬤ - ⬤ - Black Large Circle
⧭ - ⧭ - Black Circle with Down Arrow
🞄 - 🞄 - Black Slightly Small Circle
• - • - Bullet (also • - • - Message Waiting)
∙ - ∙ - Bullet Operator
⋅ - ⋅ - Dot Operator (also · - · - Middle Dot)
🌑 - 🌑 - New Moon Symbol

You can use a span with 50% border radius.

 .mydot{
     background: rgb(66, 183, 42);
     border-radius: 50%;
     display: inline-block;
     height: 20px;
     margin-left: 4px;
     margin-right: 4px;
     width: 20px;
}    

<span class="mydot"></span>