Is this phrase correct? Today was a holiday? It isn't "today is" ?

Yes, "Today" is generally followed by present tense, and the present tense of "be" is "is" :)

but i guess there are exemptions, depending on how the sentence is structured e.x. "Today was a holiday that's why we did what we did." like here, where the later half of the sentence is past tense, the first half will be as well. I'm not really sure how it works.

Ok! Klettur. In any case thanks for your help!

Klettur is correct. I've used the phrase "Today was a holiday" in the evening, after the events of the day, to explain what went on. The phrase only works after most of the day is already over, and you are explaining things in the past tense.

Think of the difference between:

"Today is a holiday, so we are going to the beach."

and

"Today was a holiday, so we went to the beach."

In the first sentence, you're telling someone either what you're doing right now, or what you will do later today.

In the second sentence, you're telling someone what you've already done today. Perhaps the person you're speaking to didn't know it was a holiday.

Thanks Galiana, for additional explanation!!!! Very good!!!!

yes, you can use the verb was if the day(today) is in the end. But, if you are at the beggening of the day, you will use ``is``

Interesting.. i read in some song hip hop style.. I ain't.. is it correct??

@RamonBA In a hip hop song, "I ain't" can be correct. In most other situations, it is considered incorrect.