Korean car manufacturers have come a long way since the 80's and early 90's. They are now reliable, inexpensive vehicles. I, personally, think that they need a little work in the style department... IMHO they are all a bit unsightly.
If you want a good inexpensive, reliable daily driver a Hyundai or Kia are both viable options. Don't expect to give them a beating though... Parts still break! The build quality seems to hearken back to the early days of the Japanese import market. The cars are solidly built with little attention paid to finery. Both Kia and Hyundai are making strides though, some of the higher-ended vehicles are kind of nice (if not still ugly).
Mazda, on the other hand, has been around for quite some time. They make very nice cars (and I like the styling 100x better than the Korean competition). Although I have never owned one, I have driven them in many forms over the years.
I, personally, enjoy the detail spent by the Germans in their cars. Even back in the day, the difference in material quality on the interiors and trim was evident between the entry level VW and most Japanese cars. Nowadays, the Japanese have a very strong market here in the states and it is built on trust... something the U.S. manufacturers abused too much over the years.
I can't say for certainty what will fit your needs, but as a suggestion (in your price range) I would recommend any of these cars...
Toyota Yaris
Nissan Versa
Mitsubishi Lancer
Ford Fiesta
The Mazda 3 and the Veloster are decent choices as well... Of course, I would chose the Mazda over the (IMHO) ugly-as-sin Veloster any day.
