YSJ is my hometown. I know the Chipman Hill area quite well (essentially the central business district), but I have never stayed in one of their properties. Chipman Hill is actually a street which runs uphill for 1 or two blocks from King Street between City Hall and the Brunswick House office tower.
Anywhere you can get to in 15-30 mins of walking will be safe. You would need to wander quite far to reach any dodgy areas.
In the daylight, be sure to visit the Loyalist Burial Grounds, King Square, then head south to Queen Square, and return via Germain Street admiring the architecture. In the evening, wander over to O'Leary's Pub.
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13F