Bonjour Vicky,

You're right that "it is nice today" would translate as "il fait bon" if you are referring to how it feels.  However, "it is nice today" could also translate as "il fait beau" if you are referring to how it looks.

When the weather feels neither hot nor cold, it feels warm.  Which is a "nice" temperature.  So, when saying "it feels nice today", it must also mean that it feels warm.  Hence, it is correct to translate "il fait bon" to mean "it is warm".

 

Here are a few examples: 

Il fait froid = it is/feels cold

Il fait chaud = it is/feels hot

Il fait bon = it is/feels warm

                 = it is/feels nice

I invite you to click on the following link where this exact point is actually very well described towards the end. 

Talking about the weather with il fait + [adjective]

Bonne journée!