Is God near and tenderhearted, or Holy and unapproachable? Yes.
For some reason, we tend to think of those aspects of the character of God to be opposed to each other. We tend to focus on either the big, glorious, and just nature of God, or His kind, loving, gracious side. We have trouble reconciling these seemingly paradoxical natures. However, Scripture is clear that although God is a consuming fire (Hebrews 12:29), He is also "gracious and merciful, slow to anger and abounding in steadfast love" (Psalm 145:8).
By the way, did you notice that I used a New Testament reference to His Holiness and then an Old Testament reference to His love? Somehow we have also gotten this false idea that the God of the Old Testament is angry, vengeful, and scary, while the God of the New Testament is all grace and no justice. That could not be farther from the way He reveals Himself in His Word.
You don't have to look any further than the cross of Jesus Christ to see God's love and justice in perfect harmony on display for all to see. Jesus Christ endured the wrath of God on our behalf in an act of unconditional, unparalleled love and grace. Besides, no matter how much we think we would want it to be true, we wouldn't want to serve a God who was loving, but not just and righteous. How could God be called loving if He did not justly deal with the evil in the world He created and eventually gave His own life to redeem?
Don't shy away from passages that emphasize a God who "dwells in unapproachable light" (1 Timothy 6:16), because it is that part of God's nature that should put us in even more awe of His love and acceptance of those who were His enemies. The fact that a perfectly righteous and just God would choose to become sin for us so that we might be made righteous (2 Corinthians 5:21) should drive us to our knees in reverence and gratitude for a God so great and so loving.
Dwelling on one of His attributes more than the others is like asking Baskin Robins to only serve vanilla ice-cream because you love it so much. But I love ice-cream too much to limit myself to one flavor; I want all 32 flavors and more! I want all of God, not just the parts of Him that make me comfortable. It's precisely in the moments that He is exceeding my understanding that I am led to deeper worship and admiration of a God so glorious.
We need a full view of God in order to have a full life of worship to Him.