"Are New Year's resolutions Biblical?"
Paul allowed the glory of the Gospel to fully occupy his mind and impact every aspect of his life, and I pray you will, too.
I'm not against New Year's resolutions, especially when they are made under the guidance of the Holy Spirit and in confidence in the Lord's power to do great and new things in and through you for His glory. As a matter of fact, from the beginning Scripture has shown that God has set times, seasons, and festivals for the purpose of renewal because God is a renewing God.
The New Testament makes it clear that we are to renew our minds constantly (see Romans 12:2; 2 Corinthians 4:16). How? By allowing the Holy Spirit to help us let go of past sin and guilt through genuine confession and repentance, by allowing the Holy Spirit of God, the very breath of God, to fill the sails of your life and be the power that pulls you through each day, week, month, and year.
Here's the problem: We can get caught in the quicksand of the past—past sorrow, failure, pain, anger, and even success—which can fill us with fear and anxiety rather than trust and peace in our faithful God. So, we must echo Paul in our every resolve: "[O]ne thing I do: Forgetting what is behind and straining toward what is ahead, I press on toward the goal to win the prize for which God has called me heavenward in Christ Jesus" (Philippians 3:13-14). Paul allowed the glory of the Gospel to fully occupy his mind and impact every aspect of his life, and I pray you will, too.