It all depends on what uniform. In the Navy/Marine Corps - No, you're not allowed to wear working uniforms (what ACU's are) off base (unless transiting). In the Army, their regs (I believe) state something to the effect of short, essential stop - which has morphed into going grocery shopping, stopping at the mall to browse, etc...
Yeah, I forgot to mention that it definitely does depend on the uniform. I was assuming it was proper liberty attire.