If Jesus is God, who/where does Jesus pray to?

Jesus was God in heaven, then became a man with no God power(except that he was born with the sinless nature of God, unlike us which have to be born again to get that nature). And when he died, became God again. When he prays, he prays to God the father(one part of the trinity) . Keep in mind that all parts of the trinity are completely equal, father, son, holy ghost(spirit).

Jesus prayed to the father like you mentioned. And he prayed to heaven.

Matthew 26:36-44

36Then Jesus went with his disciples to a place called Gethsemane, and he said to them, "Sit here while I go over there and pray." 37He took Peter and the two sons of Zebedee along with him, and he began to be sorrowful and troubled. 38Then he said to them, "My soul is overwhelmed with sorrow to the point of death. Stay here and keep watch with me." 39Going a little farther, he fell with his face to the ground and prayed, "My Father, if it is possible, may this cup be taken from me. Yet not as I will, but as you will." 40Then he returned to his disciples and found them sleeping. "Couldn't you men keep watch with me for one hour?" he asked Peter. 41"Watch and pray so that you will not fall into temptation. The spirit is willing, but the flesh is weak." 42He went away a second time and prayed, "My Father, if it is not possible for this cup to be taken away unless I drink it, may your will be done." 43When he came back, he again found them sleeping, because their eyes were heavy. 44So he left them and went away once more and prayed the third time, saying the same thing.

Jesus was overwhelmed and prayed to the father that he would be taken away from his cup of wrath. God sent a part of him down to take his own cup of wrath. It doesn't really make to much of a difference to the other people. St. Patrick said he is like a three leaf clover. He is three in one. A three leaf clover can separate itself, and still be one substance.

Much of what follows comes from the Westminster Shorter Catechism.

The Trinity

The Father, Son and Holy Spirit are 3 separate Persons (each have their own consciousness, will etc). They partake of one essence (that is what makes each Person to be God). The essence of God must never be confused with the 3 Persons Who are each God. The essence of God is not a person, otherwise we have 4 separate persons Who are God. That is not what the Bible teaches. The Bible teaches one essence and 3 Persons.

Essence can be applied to anything. It is akin to a definition. Unfortunately, it is almost impossible to define anything since we are so slow of understanding. For example, what is a chair? Does it have 3 legs and a round top? What about 4 legs and a square top? What about steel tubes that curve around...and so on and so on. I'm sure you get the picture.

So moving on from chairs, what is a rock? What is a tree? What is a human? Does a human need two arms? Does a human have to be >3 feet tall? Does a human have to have a certain IQ? You see in all these examples we are trying to understand what set of characteristics make up what we are trying to define. ie what is the essence of a chair (or a rock or a tree or a human). You will see that the essence of anything is extremely hard to define, even for a chair! Yet, the essence has to be complete in order for that thing/person to be really all that thing/person is. If you take away part of the definition (essence) then you have something else. eg take away the FULL definition of a chair (rock, tree etc) and you no longer have a chair, you have something else whatever that may be, but you no longer have a chair.

God

So apply this to God. What does it mean to be God? Well, in a very small way it means to be a Spirit Who is infinite and eternal in His being, wisdom, power, holiness, justice, goodness and truth. (obviously not a full definition). It is extremely hard to get a full definition of what it means to be God. But scouring the Bible leads us to at least a summary as just given.

Now the 3 Persons, Father, Son and Spirit each have ALL the characteristics just mentioned (infinite, eternal etc). And ONLY these 3 Persons have those characteristics. Nothing else at all has these characteristics, otherwise that thing would also be God. These characteristics comprise the essence of what it means to be God.

Summary

So if a person has ALL of these characteristics, then that person must be God.... Just as if any object has ALL the characteristics of a chair, then we say that thing MUST be a chair. It cannot be a tree, since it does not have all the characteristics of what it means to be a tree.

That is also why I can say without reservation that you and I are not God. We simply do not have any of those characteristics and we certainly don't have all of them. But the Father, Son and Spirit each have ALL of those characteristics summarised above. Thus the Father is God, the Son is God, the Spirit is God. They are equal in power and glory.

For Further Reading

Calvin in the 1500's taught what the Bible has to say on the subject (see his Institutes, Book 1 Ch13 and you can go to any good Systematic Theology to find the same answer (eg Charles Hodge, Louis Berkhoff)...

Luk 22:42 Saying, Father, if thou be willing, remove this cup from me: nevertheless not my will, but thine, be done.

Php 2:7 But made himself of no reputation, and took upon him the form of a servant, and was made in the likeness of men:

Mat 6:9 After this manner therefore pray ye: Our Father which art in heaven, Hallowed be thy name.

From the Word of Faith perspective we only pray to the Father others do it differently and we do not call them heretics nor do we actively burn people at the stake though we have been known to burn beef stakes. Jesus did not pray to Himself. Luke 22:42 shows a clear differentiation between Christ and the Father. He did not have a split personality or dissociative identity disorder nor was he a megalomaniac. He lived on this earth as a man as per Philippians 2:7. He prayed to the Father whom He was (and is) in unity with while he was anointed by the Holy Spirit. Christ needs no mediator. Our prayers are different we have a mediator to the Father, Christ Himself. We pray to the Father while we are filled with the Holy Spirit and while we are in Christ. The Father being in heaven according to Mat 6:9.

If I understand the question, it seems like it's getting at the nature of the Trinity -- that is, how does one person of the Trinity (the Son) relate to another person of the Trinity (the Father)?

The short answer to your question might be: Most contemporary Christian groups believe that the God of the Bible exists as a Trinity, so when Jesus prayed, one person of the Trinity addressed another person of the Trinity.

The extent to which that clarifies things is another question, and perhaps that's just the point: the Trinity is a thoroughly difficult concept, and theology that addresses trinitarian concepts can actually be rather confusing. It seems that efforts to come up with any sort of earthly analogy almost immediately bump into one historically defined heresy or another: tritheism, partialism, various forms of modalism, and so on. I think Affable Geek does an admirable job of explaining the "unexplainability" of the Trinity in this answer, and there's plenty of valuable content about the Trinity in a number of C.SE posts.

The most widely accepted description of the Trinity is found in the Athanasian Creed. It has a complicated history, comprehensively explained here, by vastly capable authors. (The same authors address the doctrine of the Trinity here, starting at page 18).

The Nicene Creed also provides some important info on the Trinity, including the idea that Jesus was "begotten, not made, being of one substance with the Father." That particular section confronted Arianism, another heresy.

The text of both creeds can be found in the "Three Ecumenical Creeds" section of the Lutherans' Book of Concord.

As to the location of each person during Jesus' prayers: Jesus was on earth, and the Father was in heaven. Cf. Mt 6:9.

As Matt said in his OP:

"some of Christianity believe God and Jesus to be one being, whereas some believe them to be separate and distinct beings".

Yes, these are the prevailing opinions among χριστιανους (Christians, followers of a messianic Jesus; see, e.g., Matt. 1:16; Acts 11:26). But there are other followers of the teachings of a Jesus they see as non-messianic. They believe that "God" (YHVH/JeHoVaH) is not Jesus' "Father in heaven," but a separate and distinct spiritual entity referred to by Jesus in, inter alia, John 1:18; 5:37; 6:46; 14:7-11; 16:25-31. Accordingly, when Jesus prays, it isn't "God" (YHVH/JeHoVaH) Jesus prays to, but that spiritual entity Jesus referred to as "my Father".

Several volumes were written to explain their beliefs, but they're out of print since the passing of the author in the 1990's. I could go on at length, but I think I answered (in part?) Matt's question.