Depending on weight etc., you'll go down at between 1500 to 1800 fpm in autorotation in an R44.
Airspeed for maximum range auto is 90kts. So from 2000ft agl, you'd have an autorotation range of about 1.5nm in the event of engine failure - enough to give you plenty of choices in most situations.
For single engined ops over built-up areas, the requirement for a heli is to "land safely" in the event of engine failure (as opposed to "land clear") - plus of course you still have to comply with the 1000ft rule [recently changed from 1500ft].
You mentioned gearbox failure too: sadly, that's likely to be rather more terminal - however many engines you have !