I'm going to go with
The Mississippi (River)
Explanation will follow, gradually.
Four eyes have I and a mouth of one
Mississippi are the four I's, and the river has one mouth. OP Edit: Additionally, the "M" can appear to be "mouth-like".
I do not speak for I have no tongue
Rivers have mouths but no tongues.
I have the curves to match my eyes, I'm wide and skinny to no one's surprise
Rivers have curves and have different sizes at different points. OP Reasoning: The curves to match the eyes (i's), is the four s's in Mississippi.
I may be a female given my start
This is where I'm confused, at least a little bit. Maybe it's that rivers and bodies of water can be referred to as "she," but I'm not sure. OP Reasoning: The first 4 letters "Miss" indicates a female.
St. Louis holds the bottom of my heart
The river begins in St. Louis, or at least around that area.
Two legs I have, though I cannot stand
The "legs" of a river are not really for standing. OP Reasoning: The "legs" are the p's in Mississippi.
But I think they're the finest in all the lands
The Mississippi river is the longest in the United States.