Translation:I think I am going to take a vacation this week.
In Australia, Britain and New Zealand, we would say: I'm taking some leave or I'm taking holidays, or I'm taking some time off. We sometimes use the word vacation but not in the way it is here. To be honest, the use of 'vacation' in this English translation sounds very odd to me. Perhaps it's an American usage?
No, we would never say that here either. I think this is just a mistake. The only instance it would be used would be as a direction. "John, take some vacation time for yourself." If you add time after it might be acceptable but it's a rare instance. I've never heard "I will take some vacation". It just sounds wrong.
I think that beyond the national differences noted in the comments above, the phrase also has quite different cultural or familial usage. When I think of holiday I might just as likely use vacation. (Canadian of British birth) In my mind, they imply going to a pleasant place to relax and enjoy life. On the other hand, the word 'leave' to me means a break from work or being in the forces and not necessarily leaving ones locale. I think in the true sense of the word vacation the stem is 'vacate' meaning to clear out or go away.(Google the etymology to see) All these different interpretations don't really stop us from understanding the Spanish sentence though, do they?
I don't think this is valid in this instance. "tomarse unas vacaciones" is just a phrase meaning "take a vacaction" so the reflexive part is not with ir but tomar. As Duomail points out below it could also be written "yo voy a tomarme unas vacaciones."
The “me“ belongs to “tomar“, this sentence may be rephrased as “voy a tomarme unas vacaciones“ (I'm going to...). I think that “I'm leaving to take a vacation“ could be “me voy para tomarme unas vacaciones“, “estoy saliendo para tomarme unas vacaciones“ or just “me voy a tomarme unas vacaciones“, though not so clear (explicit) as the first two.
I have been told that it is normal to use the plural where we would say a vacation. I think that 'a vacation' is a collective term in English so it can refer to one day or many days. Perhaps, on the other hand, if you are talking about a vacation from work you might say, for just a few days, 'vacation days'. If you were to say to me 'a few vacations' I would assume you were going to take several vacations. Here's SpanishDict.com's translation for vacation(singular in English) https://www.spanishdict.com/translate/a%20vacation 'vacation days' https://www.spanishdict.com/translate/some%20vacation%20days 'several vacations' https://www.spanishdict.com/translate/several%20vacations
It's good to be technical because as you explore another language you may also get some insight into the way your own is used. Buena Suerte/Good Luck with your studies.