Based purely on linguistic data, the most neutral accent in the US in that of southern and central Iowa, and parts of the neighboring states to the east and west. Although national news anchors have been known to study the accent in order to cover the entire country, please note that this is in no way a prestige dialect analogous to the British “RP.” In reality, regional American accents are almost never an issue for native speakers — the situation in the UK may be radically different. The only Americans who use strong regional accents are a relatively few elderly elderly people living in the more remote regions, but even this is disappearing under the influence of the mass media and the internet. Keep in mind that US (and Canadian) society is extremely mobile, socially, economically, and geographically, so accent is absolutely no big deal whatsoever. Good luck in your further English studies! If you have additional questions, you know where to reach me.

a neutral accent in America is called a "non-regional dialect." You're most likely to hear it on national news casts, like CNN, NPR, or Voice of America.