One of the advantages of living in the DC area (you know, in addition to the reasonable beltway traffic and amicable politicians...) is that I could get a pre-commissioning physical at Walter Reed military hospital in Bethesda in lieu of MEPS. That was a two-step process; about a half day of blood labs, hearing and visual tests, dental exam, etc, followed by a one-hour review of results with a doc a couple weeks later. My recruiter needed to set up the initial appointment but from there I was able to do all of my own scheduling directly with the hospital, just like in the civilian world.
I highly recommend that path if you can get it - the whole process was very efficient, saved me from taking a bunch of leave (0730 appointments before work FTW), and the hospital staff treated me like a human being throughout.