I want to know if the sentence
On my father's belly is the best place to sleep
Can preposition phrase On my father's belly be subject in the sentence?
When the main verb is BE, and the constituents on either side are noun phrases, it can be difficult or impossible to determine which noun-phrase is subject and which is a predicated subject complement. But it doesn't really matter because BE predicates an equality.
The sky is the best place to find stars.
The best place to find stars is the sky.
High up in a tree is the hardest place to retrieve a cat from.
The hardest place to retrieve a cat from is high up in a tree.
In a small boat on a choppy sea is an easy place to get seasick.
An easy place to get seasick is in a small boat on a choppy sea.
At a dim bar with a cold beer is his idea of the place to be.
His idea of the place to be is at a dim bar with a cold beer.
As Tᴚoɯɐuo pointed out, it typically doesn't matter which way you construct the sentence. What you wrote is grammatically correct. However, a native speaker would phrase it the other way: "The best place to sleep is on my father's belly" Starting with a prepositional phrase like this sounds a bit awkward. Any native speaker would understand exactly what you meant by "On my father's belly is the best place to sleep," but they would likely say it the other way around unless they had some ulterior reason to do otherwise. They also might drop the word "on" and simply say "My father's belly is the best place to sleep" and assume that context is enough to let the listener know that they're talking about sleeping on their father's belly, rather than in their father's belly or around their fathers' belly, or any other preposition.