I am stunned at how many introductory books there are. My recommendation is William Bolstad and James Curran's Introduction to Bayesian Statistics. It has several nice elements to it.

First, it covers a large percentage of the conjugate problems and covers all the standard problems in a sophomore-level test for an introduction to statistics course. It also covers the case when the prior is not conjugate.

Second, it covers the appropriate Frequentist procedure at each point, explaining both.

Third, it derives the solutions and so allows an understanding of the issues at a deeper level. It, optionally, allows for rigor.

It covers everything a sophomore-level book would cover, except with underlying math included. It is an upper-division, lower master's level book due to the included math.