I personally believe that El-Guest has the correct answer above; I would like to throw in another possible answer; though it doesn't meet all lines.
Mono Lake in Mono County - California
Near a faith's top spots, I'm not quite a sea;
Couldn't really find an answer for faith here; but it is a lake.
I contain water more seasoned than shchi.
It is a saline soda lake.
As you jump in, you will float like a flea.
As El-Guest stated, this is due to the salt in the water.
A basketball goat wanders right into me.
Basketball Goat could be referring to Earl Manigault (his nickname was literally The Goat) who was a big influence on Kareem Abdul-Jabbar of the LA Lakers. However, I like rhsquared's response to this and agree that this refers to Michael Jordan.
A big city's namesake, that should prove a clue.
Mono is a county in California, not a city so it doesn't truly fit here.
I'm far from the Near East, and far from dead too.
It's located in the United States, and it supports aquatic life. Also, as El-Guest stated, it is not the Dead Sea.
Note: If you downvote, please leave an explanation as to how I can improve my post. I only added this answer because it was interesting.