One thing I ask of the LORD, this is what I seek: that I may dwell in the house of the LORD all the days of my life, to gaze upon the beauty of the LORD and to seek him in his temple.

I am still confident of this: I will see the goodness of the LORD in the land of the living. Wait for the LORD; be strong and take heart and wait for the LORD.

So Davids really just got two things to ask the Lord: To save him from his enemies, and mostly, To dwell in the house of the Lord forever.