This is mostly answered by decision theory. The approach is that you must formalize what you want to achieve with your point estimate, and that can be formalized as a loss function. Examples are squared error loss: $$ L(\hat{\theta}, \theta) = (\hat{\theta} - \theta)^2 $$ absolute value loss, or others. Then the optimal estimator (in your bayesian setting) is given by the function $\hat{\theta}$ that minimized posterior expected loss: $$ E L(\hat{\theta}, \theta) $$ where the expectation is over the posterior distribution of $\theta$. In the case of the squared error loss, that is the posterior expected value. You can read about this an any text about Bayesian decision theory, such as C Roberts: "The bayesian choice" (Springer).