Hello, 

I am doing the same thing. If you are studying MSA you can go to any country: that is the good news. So Morocco might be your best bet as the cost of living is not prohibitively high. Other safe(ish) countries popular for study seem to be Tunisia and Egypt (less safe these days). Otherwise Lebanon and Jordan are relatively safe, but 'troubled' by the effects of the status of neighbouring countries. Lastly there are the Gulf countries: Oman, Qatar, Bahrain, UAE which are very safe. On the other hand they are very expensive, and have a VERY high non-Arab speaking proportion of the population. So Morocco might be your best bet overall. Obviously if you want to learn a particular dialect at the same time you have to go to that region. If you really want to learn Levantine Arabic you would probably be best going to Lebanon or to Jordan.

I hope that that is helpful. 

Aliph: Morocco was part of the kingdoms of Amazigh (berbers), those were the people that lived in North Africa before the Islamic conquest. After that many arabs came to live in Maghreb, and as they did so, they didn't expell anyone and kept living side to side with Amazighs.  Now, what my fellow citizen meant is that Moroccan dialect was not influenced by Tamazight (Which is the language spoken by berberes), and that no one's gonna speak Tamazight with you, which is completely wrong. Moroccan dialect has many Berbere words:

mezloot=Poor, Wakha=Ok, Saroot=Key, Fekroon=Turtle, Ghwat=Crying,...

These words are used in our daily conversations and have Nothing to do with arabic.

There still are Berbères who can't or refuse to speak Moroccan Arabic (Darija) and prefer to speak their native language (berbere) which a Moroccan from Casablanca or Rabat or Fes cannot understand at all.

To summarise, In morocco there have been two ethnicities, one was living in Morocco, and the other came from Arab peninsula and lived together with Amazigh. After centuries, ther have many mixed mariages between the 2 nations, and it all got mixed. as a result, the arabic of the arabs coming from the east got influenced by Tamazight (by other foreign languages as well) and so was born the Moroccan dialect. But some people who chose to live in the countrysides, in the mountains of Rif and Atlas, managed to conserve their culture and their language, and keep using it in their daily lives, sometimes with some sort of overpride, so logically they'd refuse to speak to others in Arabic.

I was studying at an institute, but at the moment I have a private tutor.  I am in a town other than Amman, because there is less English spoken.  If you are interested in Jordan, Google Arabic language schools, there are many.

This Omani language school looks interesting http://www.noormajan-institute.com