Unless your running EFI or have a stereo you should have only a couple circuits not cut off by the ignition. The "keep alive" memory for a computer (EFI) or the stereo will typically be less than 1ma (1/1000A). (leaking ign. switch is possible)
As stated, a leak at the alternator or regulator, starter solenoid, lights. While monitoring the battery voltage, pull fuses and disconnect the alt big lead. You should notice a couple tenths of a volt jump when you interrupt the leaking circuit.
Most DMM's have a 200ma current scale and usually a 10A scale, start with the 10A and work your way down. (placed in series with battery cable)
The big thing about batteries is the Amp/hours rating (not the CCA rating which is marketing BS for the most part). Typical car battery is in the 85 ~ 100 A/hr range: (1 amp for 100 hrs, 10A for 10 hrs, 100A for 1 hr.... You get the idea).
You'll probably find a leak of .5~2A from what your describing.
Worst thing they ever did was move from ampmeters to voltmeters on cars. (but hey, 12ft of 10ga copper wire is darn near $5!!)