The Bible does not explicitly state whether Adam and Eve went to Heaven. While Adam and Eve later serve as examples of sinful failure in the rest of Scripture (Adam in Job 31:33, Hosea 6:7, Rom. 5:12-14, 1 Cor. 15:21-22 and Eve in 2 Cor. 11:3, 1 Tim. 2:13-14), we do know at least two instances later in the Genesis narrative where Eve exhibited faith in God.
In our first example, Eve believed that God was going to send her a promised child, referring to Cain,
"Now the man had relations with his wife Eve, and she conceived and gave birth to Cain, and she said, 'I have gotten a manchild with the help of the LORD,'" (Gen. 4:1).
From this first passage, we see that Eve trusted in the promise of God to provide a child.
However, tragically, Cain actually kills Abel, and God expells him from the presence of Adam and Eve (Gen. 4:12-16). Not only has Eve lost Abel but also she lost her firstborn son, Cain. Despite her dire circumstances, Eve continues to trust God to provide. We later read,
"Adam had relations with his wife again; and she gave birth to a son, and named him Seth [which literally means "appointed"], for, she said, 'God has appointed me another offspring in place of Abel, for Cain killed him,'" (Gen. 4:25).
Again, Eve continues to rely on the promise of God. This time she actually receives the "appointed" child who did not cause the heartache which Cain caused her.
Eve as an Example of Faith
According to the Bible, humans were always justified (made right or saved) before God by faith (Gen. 15:6, Rom. 4:1-11, cf. Heb. 11:6ff). Therefore, since Eve believed in the Lord, there is good reason to believe that she was saved. Eve, in spite of her initial failure in the Garden of Eden (Gen. 3:16), can certainly serve as a model of faith and trust as a result of her later actions of faith in the Book of Genesis (Gen. 4:1, 25). If Adam followed her wise example, which is likely since it was through him that Jesus came (Luke 3:38), he also would have been saved.
In Genesis 3, Adam and Eve sinned against God by eating the fruit from the tree of the knowledge of good and evil. After they sinned by eating the fruit, they became aware of their sinfulness and sewed fig leaves together to cover themselves (Gen. 3:7). Then Adam and Eve, " . . . heard the sound of the LORD God walking in the garden in the cool of the day, and the man and his wife hid themselves from the presence of the LORD God among the trees of the garden," (Gen. 3:8).
It is quite likely that the reference to "the LORD God walking in the garden" refers to the preincarnate Jesus. This preincarnate Jesus then made atonement for Adam and Eve by providing animal skins as a covering for them. "The LORD God made garments of skin for Adam and his wife, and clothed them," (Gen. 3:21). Typologically, these two passages (Gen. 3:7 and 3:21) may be a reference to man's failed attempt to cover his sin by his own actions (fig leaf coverings), but God providing His own covering (shedding of blood for the animal skins, Lev. 17:11, Heb. 9:22) with an implied sacrifice (death of an animal to provide a covering, which points towards the once for all sacrifice of Jesus). If this is the case, then Adam and Eve would both have been saved.