Here's some observations comparing Malaysia and South Korea having lived in both ~6 months or more (note: Kuala Lumpur and Incheon/Seoul respectively, other cities will certainly have different characteristics):
South Korea is definitely more homogenous in terms of local community because it was very xenophobic for a long time after its history of being ravaged by various neighboring countries, and only in the past decade has the international scene really exploded--considering the many expats who go to teach English and the country's high demand for such teachers. Malaysia on the other hand was colonized a few times over by the Portuguese, British, and Dutch centuries ago.
An expat can live in either country without learning the local language(s), but there is a noticeable difference. In Malaysia your friend would find a bigger population of fluent English speakers (which can be a huge relief in the face of culture shock) while, in Korea, people may be more reluctant and shy to speak in English. Malaysia just has the longer history and incorporation of English vs Korea where English is truly a second language.
Granted, the further your friend gets from KL and the main cities, the less prevalent English may become (like Kuno describes his Northeastern experience).
In terms of safety:
I confess that as a female, I rarely walk alone at night, even back in the States. In this regard, Korea and Japan were the few exceptions because there really is so little crime. Still, I think your friend will be perfectly fine in Malaysia.
Again, Kuno pretty much nailed it on the dot. The main safety concern in Malaysia is getting a purse or phone stolen. I always walk with my bag facing the wall (or away from traffic) and have never run into any problems. However, I witnessed a friend have her purse (and passport, credit cards, everything) stolen from her chair while chatting over a drink in Changkat, literally from under our noses. Everybody knows somebody this has happened to, and the stories spread to encourage common sense when walking/traveling in Malaysia.
Let me rephrase that (b/c common sense is not so common) to say one needs to be pragmatic. It's good to have a copy of one's passport and perhaps even a second wallet, so that if one's purse does get stolen, it's a shame, but there's always a back-up. And, even in my friend's case, the situation was invasive, frustrating, and a hassle, but she ended up canceling her cards, getting a replacement passport from the embassy, and working with her bank (HSBC was awesome in this situation) to get replacement cards shipped within a week.
There's also different cultural standards.
...such as wearing revealing clothes. Both Koreans and Malays tend to look down on low cleavage or bared arms or short shorts/skirts, but you'll see it in both places. In Korea, there's a funny cartoon with a Western girl and a Korean girl glaring at each other; the Korean girl comments on the Western girl's shocking low cleavage, while the Western girl comments on the Korean girl's patch of a mini-skirt. In Malaysia, there's a whole diversity of clothes: Muslim women wearing tudongs, non-Muslims wearing skirts, shorts, or revealing shirts, and everybody in between. If a girl wears something revealing, let's be honest, people will stare regardless of the country.
I've yet to be afraid any more than I would be in the States. If anything, living in S Korea and Malaysia have led to two very different, interesting experiences--and an amazing education on international diversity.
I'd 100% encourage your friend to experience Malaysia, if for any reason, to break any preconceptions/misconceptions in exchange for a "wow" factor. She may love it or hate it, but I guarantee that she will be a changed person by the end of her scholarship.
As for the specific states, I can't provide much, but have heard good things about Johor. And the plus side about the Eastern states may be that she can escape to the stunning islands off the Eastern mainland for weekend getaways, too. I have briefly traveled through the Northeastern states, and though more conservative, as everyone else is saying on this forum, people were incredibly friendly. ;]
If she still prefers to go to S Korea, there are many opportunities (perhaps minus the Fulbright backing) that she can find a recruiter to place her in a good Korean school.
Hope this helps~~ ^^