Halliday & Resnick Fundamentals of Physics is what we used in AP as well as in freshman year at college. Covers most sections one needs to be familiar with to be physics literate (solid/fluid mechanics, waves, thermo, electromagnetism, optics, relativity).
Is that still in print? That was the physics book we used my freshman year, in 1974. It was a great book. I’m still sorry I sold it.
That was my first year text book in 1998. Sounds like it's still going strong!
Still used in as an undergraduate in 2013
Jearl Walker (of Cleveland State and PBS’s Kinetic Carnival) was added as an author.
For the mathematically inclined, the best I've seen is An Introduction to Continuum Mechanics by Morton Gurtin from 1981. At one point, it could be purchased from Google books directly as a pdf.
I don’t know much about continuum mechanics (unless you count stat mech but I wouldn’t), however Goldstein has a few chapters on the topic that might serve as an introduction