There isn't just one best feeling for me, it's multiple actually to be honest.
Pure, unadulterated, raw, happiness. Felt when your soul is touched by something so beautiful, so rarely and truly felt that bewilderment is what first comes to thought before the actual realization of happiness is felt.
Inspiration. The feeling you get when something inside you clicks, like a breath of warmth felt throughout your body. Your heart rate picks up in pure joy and awe and your brain is fueled with so many wonderful feelings and thoughts. Tears form and fall at the pure contentment you feel as you become inspired by such simplicity at certain momentous times.
Accomplishment. That feeling of relief, it's all done. All the struggles, the tears, the pain and disappointments you felt disappear once you've felt accomplishment. This is when the feeling of happiness kicks in and the struggling-to-hide tears fall and keep falling. You feel an amazing amount of pride and joy for yourself and can see the same pride and joy you feel beaming in the eyes and hearts of your loved ones.
Love. When you feel that others care deeply for you. When that pang in your heart isn't one of inner loneliness anymore but one of happiness and joy. When you see and feel that someone you deeply care for shares that same feeling with you. The feeling of love is the feeling of being understood and accepted unconditionally for who you are. Love, when felt is genuine, deep, and sincere.
I'm moved easily. I'm sure there are many more "best feelings" I have than just these.