i really loved neutral bay when i lived there when i was younger. keep in mind i have the perspective of it as from a 10 year old...
but it's got a great community with a huge street with shops and cafes and restaurants, 2 woolies and 1 coles. Forsyth park right down the road, and it is *walking distance* to st leonards too. It also has really huge bus stops in it (Neutral bay junction and Military Rd/ Wastons street) which have express buses to the city that take like 10 mins. the only downside is the closest train station is wynyard (10-20mins bus) or st leonards (15-25 mins by bus) :/
don't know much about the crime rates and all that, but i felt relatively safe walking round on those roads as a little kid. the only thing is that military road is really busy, so dont be an idiot who jaywalks