Stay at home.
When “home” functions as an adverb, it can modify the verb “stay”. There are other examples, such as “go home”,but there is no expression:
Go to home.
So I wonder which one is correct?
People used to think that prepositions had to come before a noun. However, in 1924 a writer called Otto Jespersen realised that prepositions are always prepositions, even if we don’t use them with a noun. He also realised that some prepositions never come before nouns.
It took a long time for people to change their thinking. Now, if you look in a modern grammar such as:
- The Cambridge Grammar of the English Language Huddleston & Pullum, 2002
- Oxford Modern English Grammar, Aarts, 2011
… you will see that prepositions are a class of words like nouns, verbs and adjectives. It doesn’t matter what kind of words we find them with.
Home in English, is a preposition. There is another word home which is a noun. We can use prepositions and preposition phrases as the complement of the verb BE:
- She is in
- She is in the bath
- She is out
- She is inside
- She is inside the shop
- She is away
- She is around
- She is about
- She is abroad
- She is home
Prepositions can take other preposition phrases as a complement. In other words we often use two prepositions together:
- She is out of touch
- She is away from her desk
- She is round about somewhere
- She is at home
The Original Posters examples
The verb STAY usually takes a locative complement. Usually this complement is a preposition phrase. The word at and home are both prepositions. The sentences:
- Stay home
- Stay at home
… are both grammatical.
The preposition to is unusual because we usually need to use it with a noun. So we see:
- Go to work
- Go to the shop
- Go to a concert
The word to can’t usually come before another preposition:
- *Go to inside
- *Go to away
- *Go to out
- *Go to abroad
- *Go to home
- *Go to at home
Notice, though that if we use the noun home instead of the preposition home, then we can use the preposition to
- Go to my home
- Go to different homes in the area
- Go to homes before you buy them
- I went to an old peoples home.
Hope this is helpful!