Differentially private location trace synthesis (DPLTS) has recently emerged as a solution to protect mobile users' privacy while enabling the analysis and sharing of their location traces. A key challenge in DPLTS is to best preserve the utility in location trace datasets, which is non-trivial considering the high dimensionality, complexity and heterogeneity of datasets, as well as the diverse types and notions of utility. In this paper, we present OptaTrace: a utility-optimized and targeted approach to DPLTS. Given a real trace dataset D, the differential privacy parameter epsilon controlling the strength of privacy protection, and the utility/error metric Err of interest; OptaTrace uses Bayesian optimization to optimize DPLTS such that the output error (measured in terms of given metric Err) is minimized while epsilon-differential privacy is satisfied. In addition, OptaTrace introduces a utility module that contains several built-in error metrics for utility benchmarking and for choosing Err, as well as a front-end web interface for accessible and interactive DPLTS service. Experiments show that OptaTrace's optimized output can yield substantial utility improvement and error reduction compared to previous work.