Simpson Bay is usually a safe area, although I would not walk the back streets at night. I have walked the back streets and beach in this area during the day many times and never a problem. In Nov. I stayed at The Horny Toad, which is off the same road but more towards the airport, with no problems. There are a few restaurants in the area you are looking at with Sublime being one we really enjoyed. Other comments on your question cover the area and situation very well.

I would be concerned about the beach (or lack thereof) in the area you are considering. In Nov. I attempted to walk from The Horny Toad to basically the bridge via the beach and ran out of beach in the area you are considering. A few years ago the beach was there and it was an easy walk but the beaches change. Not sure what the current status is in that area but there had been a lot of erosion.