"I will take a break today."
does 休み mean "take a break" as well, or just "break"? because I felt there was no verb in the sentence [今日は休みます]
休む (やすむ) is a verb meaning "to take a break, to rest," and that is what's being used here. The polite form is 休みます.
The verb is actually 休みます。It's a polite conjugation of 休む, which means "to rest, to take a break". 休み in this case is actually the verb stem, which can sometimes act as a noun.
休む means "to take a break", which is a verb. 休み alone means "a break", and is a noun (in this case I think it is formed from the verb by taking the verb in polite form and removing the -ます part. I've seen some other words which are like that)
This is a verb where the noun form is simply the verb in い form. So 休み is a break and 休む is to take a break.
Another verb I know that does this is 始まる(はじまる) which is "to begin" , but when changed to 始まりmeans "beginning"