It isn't important to completely eliminate your accent to speak English in the U.S.. There are many native accents across our country, and we are accustomed to meeting people from all over the world. There are many acceptable ways to speak English, not just one way.
I want to read, write and understand Korean. I self-study everyday. The biggest challenge for me is speaking Korean, but I would like to learn enough to comfortably travel there on my own and not feel isolated.