I like to think of philosophy, not so much as the study of / search for TRUTH, but as the study of what the best ways to find truths might be. Truth is still the centerpiece, but in a more meta-way.
How can we find out what's true? If this person says this is true, and that person says that is true, how can we tell who we should believe? Maybe this person has evidence - should we care about evidence? Why? Maybe that person can show that this other person's beliefs are internally inconsistent, contradictory - should we care about consistency? Should we care about contradictions? Why?
Why should we care about evidence, consistency, contradictions? Why should we care about parsimony and simplicity?
And how can we turn our tools of thought in on ourselves, and investigate the questions of our own biases?
I think these are some of the most important questions for Philosophy to answer - not What's True?, but instead, What are our tools to find and distinguish truth, and why should we trust them?