How good are you at judging books without knowing the topic? :) Because I kept a list of books I considered good, but cannot recall which one were good for undergrad. If you need to learn statmech from a physical point of view, I strongly recommend a book with enough mathematical details! Otherwise you waste time reading vague explanations and later you will pose yourself many unanswerable questions, which can only be derived with maths. Then you have to reread a "real" book again. Often the top recommendation from the course is closest to the syllabus, but incomplete in explanations or badly structured.
So here comes the list. If you have access to a good library go and look through those books.
The titles are usually "Statistical mechanics" or "Statistical physics" or similar. The authors are
Reichl (I think thats one I liked much)
Schwabl (fairly new book and I believe its popular in German courses)
Reif (it was my first guess for a good book, but for whatever reason I forgot to tag it "good" in my list)
Feynmann (might to too far from current days syllabus)
E.M. Lifgarbagez and L.P. Pitaevskii
Honerkamp (made a good impression in my first glance but I didnt actually read it)
Huang (made a good impression in my first glance but I didnt actually read it)
LeBellac and Mortessagne ("Equilibirium and non-equilibrium statistical thermodynamics"; made a good impression in my first glance but I didnt actually read it)
Unfortunately I don't have access to a library now to judge the books again.