Hong Kong is one of the safest cities in the world. If you'd be comfortable on your own in Chicago or San Francisco or Paris, you'll be fine in Hong Kong. You might want to avoid walking on Nathan Road in Kowloon between the Sheraton and Kowloon Park -- it's not dangerous, but there are some pushy touts trying to sell watches and suits who make some people feel uncomfortable.
I'd recommend any of the hotels in Pacific Place (the Island Shangri-La, the Conrad, or the Marriott), because you would have direct access to an upscale shopping mall and to the subway system.
If you feel adventurous, you could indeed go to Shenzhen China for the day. Travel time is about 30-40 minutes each way, and it takes another half-hour or so to go through the immigration/customs dance. The shopping there can be fantastic. You would need to get a visa before you go, and I'd strongly recommend buying the
Shop in Shenzhen book by Ellen McNally.