To expand on the alternator diagnostics a bit: the output voltage is load and temperature-dependent, so the measure is expected to vary. You should see 13.7-14.1 VDC measured across the battery terminals with the car running with the headlights on.

You can also easily test for voltage drops from bad cables by measuring the output at the back of the alternator (where the thick red wire is connected) and comparing that to the between-terminals measurement.

Shop around a bit for the voltage regulator replacements-- there's a lot of variability in the prices. HUCO is a good aftermarket supplier. For some alternators there are different output set-points-- standard seems to be 14.1 VDC, but I have seen some with higher output (good for Ontario and our weather extremes!).

Good luck!