King David was a man after God's heart:
1Ki 9:4 And if thou wilt walk before me, as David thy father walked, in integrity of heart, and in uprightness, to do according to all that I have commanded thee, [and] wilt keep my statutes and my judgments:
1Ki 14:8 And rent the kingdom away from the house of David, and gave it thee: and [yet] thou hast not been as my servant David, who kept my commandments, and who followed me with all his heart, to do [that] only [which was] right in mine eyes;
Act 13:22 And when he had removed him, he raised up unto them David to be their king; to whom also he gave testimony, and said, I have found David the [son] of Jesse, a man after mine own heart, which shall fulfil all my will.
so it would be safe to assume that if David died which he did then he would be in heaven if indeed we are wrong about what happens when we die.
Now listen to What Peter says \under the guidance of the spirit on pentecost.
Act 2:24 Whom God hath raised up, having loosed the pains of death: because it was not possible that he should be holden of it.
Act 2:25 For David speaketh concerning him, I foresaw the Lord always before my face, for he is on my right hand, that I should not be moved:
Act 2:26 Therefore did my heart rejoice, and my tongue was glad; moreover also my flesh shall rest in hope:
Act 2:27 Because thou wilt not leave my soul in hell, neither wilt thou suffer thine Holy One to see corruption.
Now notice that Peter is reasoning with them that David prophesied about Jesus and not himself:
Act 2:29 Men [and] brethren, let me freely speak unto you of the patriarch David, that he is both dead and buried, and his sepulchre is with us unto this day.
Act 2:30 Therefore being a prophet, and knowing that God had sworn with an oath to him, that of the fruit of his loins, according to the flesh, he would raise up Christ to sit on his throne;
See here that he says that David is both dead and buried even now. now some may argue that its just his body but clearly there is no indication that that is the case here. In fact what peter says next proves this.
Act 2:34 For David is not ascended into the heavens: but he saith himself, The LORD said unto my Lord, Sit thou on my right hand,
and there it is, David is not in heaven he is still dead and in the grave after Jesus had been resurrected and went to heaven.
Blessings.