There are some objective ways to test your relationship with God - He was kind and wise enough not to have it all subjective.
Let me begin by stating the obvious (or the should-be-obvious): relationships have a lot of subjective elements in them. This is certainly true in my relationship to God. As a pastor, I get quite a bit of the "I just don't feel very close to God" conversations. While I can't help a person feel closer to God, I can help them put into practice disciplines that will help them actually and truly grow closer to God.
One more clarification: when we talk about "closer to God," we're not talking about distance. God is no nearer or farther from any one point in the universe than He is any other point. It all exists in Him and He is omnipresent. This "distance" is more about our interactive experience with Him and the appropriate objective and subjective things that come out of that interaction.
So, with that in mind, let me outlay a few objective questions you can ask yourself to diagnose yourself and your "closeness" to God. God knew we couldn't pull off this diagnosis on our own so He gave us some outside input. I'll pull these right from the red-letter part of the Gospels...
Is your allegiance to God above yourself, your relationships, and your possessions? (Luke 14.25-33) How would you measure this? By assuming God would ask you to do the most radical thing, and measuring your inclination toward it. Move to Africa? Forgive your parent? Surrender to ministry?
Does the Good News of Jesus come out of your mouth often and naturally? (Matthew 4.19) If Jesus calls us, He promises to make us fishers of men. These are not people who lure people in but who catch others up in something larger than any of them. In coffee shops and Kroger, driveways and dance recitals - you share not because you plan to, but because that's what's in your heart and comes out (cf. Matt. 12.34).
Do you enjoy God's Word? (John 8.31-32) When you open it, do you revel in its Truth, somehow express gratitude for the conviction it brings, commit to obeying it because you know it lays out the way of real freedom? When you don't intake it, do you miss it like you miss food when you skip lunch?
Do you hate sin? (Mark 8.34-37) When you see it in yourself and in culture, does something rise up in you that wants to kill it? When you repent, do you do so with sadness? Do you ask God for wisdom as to how to put it out of your life?
Does your spending reflect your confession? (Matthew 6.24) When it says the treasure is where the heart is, that's a real, clarifying, diagnostic question for us. Do my spending priorities reflect Kingdom priorities? Do I give a tithe (10% of my earned income) to my local church and do so gladly? When other needs come up, do I pray about them first or see what's in my checkbook first? And for all wondering, paying your bills and doing so on time is a huge part of your spending reflecting your confession. Being out of work is one thing. Being a poor steward is another.
Do you long for Jesus to return? (Mark 13.34-37) Even though it'd be as rough as anything we've ever known beforehand, even though it will bring persecution and trouble, even though it would mean the eternal end for some, do you want Jesus to return to set things right? When you see sin and sickness and senselessness, does it prompt a prayer that asks Him to make it soon?