My very favourite sight in Hong Kong (Kowloon side) was the Chi Lin nunnery and Nan Lian gardens (these are connected). On the Hong Kong side, I liked Victoria Peak (accessed via the Peak Tram).
I also liked taking the Duk Ling (a "junk") across the harbour (touristy, but, you know, I was a tourist), and seeing the harbour light show from the Walk of Fame. You can take the Star Ferry across the harbour, also (or the MTR beneath it).
I also really enjoyed our day in Macau (about a 1 hour hydrofoil ride from Hong Kong). We walked up the Rua de S. Paulo to the ruins, having traditional pork on a ciabatta bun on the way. I also spent the afternoon in the Venetian with my daughters while my husband gave a presentation at a school nearby. Wow! It's amazing. We didn't go into the casino, but shopped along the canals.
We stayed in a vacation apartment in the Causeway Bay (aka Wan Chai) area. We loved it. Every time we went over to the Kowloon side, we were happy we were not staying there. There are some decent hotels in the area around Causeway Bay and near Victoria Park, also. A friend of mine recommended the Rosedale.
However, if you don't mind staying on the Kowloon side (where the area with lots of hotels attracts a lot of beggars and hawkers), then I second the recommendation of the Y. There's a huge mall nearby. I forget the name. In Causeway Bay, Times Square is another big mall, and it has some designer stores (Fred Perry, Burberry, etc.) and Island Beverly is more trendy, with dozens of teeny-tiny boutiques spiralling around the different floors. The Pedder (sp?) was recommended as a good place to get designer stuff for cheap, but I wasn't that impressed, and you need to watch for knockoffs there. At the Ladies Market in Mon Kok, there are blocks and blocks of knockoffs for sale (I was constantly greeted with cries such as, "Hello, missy! You buy copy watch?"), along with souvenirs, clothing, etc. It's fun to bargain via calculator there. There are also places in the Kowloon side where you can get custom-made clothing, and they'll even keep your measurements so you can order from home in the future, but I can't recommend any, since I didn't try them.
There is shopping everywhere in Hong Kong. I didn't go anyplace where there wasn't plenty of shopping nearby.
A tip: get an Octopus pass for transit. You can get it at the airport right after you exit customs. It's good for MTR (subway), ferry, bus, tram, airport train, and others (8 modes of transportation in all--thus the name). (Note: The airport train meets up with the MTR at at least 3 points, if I recall correctly. When you return to the airport, you can actually check your luggage directly through to your flight before you board the airport train. So civilized!)