As I have already explained in this previous article, that every single experience count in a C.V. (for more advices about the C.V., go here -wip-).
In my article of what to do once you have your degree, that you can read here, I told you that experience is very important.
And studying or working abroad is very significative experience.
Here we are entering a very personal matter, as I am someone who had has not the opportunity to going abroad, and I am craving for it.
I am now looking for a work on a foreing country.
Anyway, precisely because I didn't go abroad, I can tell you that missing this opportunity is not a good advice.
As said, all the experencies are important, and having left your home country, for a brief or for a longer time, is always well noted.
I would advice to do it as soon as possible, both for those who don't want to leave for a long period as well as for those that want to directly leave their country and live abroad.
Why? Because it will give you an early vision of the reality of what adult life means, because if you really don't want to leave forever, you'll know it and will have a short experience abroad that will still count on your C.V. and will teach you many valuable lessons, and those lessons are the ones the enterprises are seeking,
On another hand, if you want to leave, it will only give you a preview, so you will be more prepared later, and furthermore, it will be easier to go. Sadly, the fact of not having been able of doing an Erasmus or a Master abroad during my study years (for personal reasons), gives me fewer opportunities or leaving the country now.
I am not worried, as I still look for interesting offers and count on my profile and background. In any case, if I do not find something directly from here, I am saving money, so in a couple of years, I will leave and directly go to another country and search for a job there. But that doesn't mean it will be easier if I already have that experience.
So my advice would be to at least do a short stay away, if only for a few months.
If you have more doubts, about the benefices of going abroad, I'll leave you here some useful links to my other articles about the subject.