The time suits me well or fits me well?

You would say "The time suits me well."

From Merriam-Webster:

Suit (verb)

: to provide what is required or wanted by or for (someone or something)

: to be proper or suitable for (someone or something)

: to be attractive on (someone)

When you say that a certain time suits you well, you're saying that that time is suitable for you.

On the other hand, if you say something fits you well, you're either literally talking about clothing that fits your body, or you're figurative talking about a trait that "fits" you or seems like it could be applied to you. A Google search of "fits me well" brings back results to this effect, for example "This shoe fits me well" (This shoe fits my foot well) and "I think this offense fits me well" (This position fits the skills that I have).