I was in Nassau in May and July, anchored on the west end for several weeks. You can use the free dinghy dock
at the Texaco next to Nassau Yacht Haven or motor
down to the Green Parrot's larger dock (preferred).
When we were there the grocery store across the street near the Starbucks was closed but I was told it would reopen soon (remember "soon" is a relative term). Otherwise it's about a two mile hike to the nearest big store (hike there - taxi back). Holding is alleged to be poor in the west anchorage but I rode
out several nasty storms with no trouble. Holding is supposed to be better by the Green Parrot, but it is often crowded.
As for security
we had no issues and covered many miles on foot, though not after dark. A chain around your dink and motor
is advised, as is pulling it up at night and locking the thing.
The locals are quick to tell you areas of town to avoid and common sense goes a long way. Affect the look of a scruffy sailor rather than a cruise ship
tourist. Lock your boat when you leave.
Nassau can be a dangerous place for idiots who stagger to their boats shitfaced drunk at midnight - or engage in similar stupid behavior, but it's no different than any crime ridden major US city.
Just be smart, take reasonable precautions and enjoy. It's a neat place for a few day's wanderings, albeit a bit on the touristy side.
PM me if you'd like some more info. I was stuck there quite awhile due to weather