The general advice on Tripadvisor (I think you said you started there) is good for the obvious don’t misses. Also the website Discover Hong Kong was a source for me for hikes, walks, more out of the cultural and historical sites, etc. The biggies are probably pretty obvious - Victoria Peak, Lantau Island Big Buddha, 10,000 Buddhas in Sha Tin (the New Town Plaza there at the MTR station is also a good shopping place for clothes that fit Americans, familiar brands and reasonable prices), Kowloon’s Chi Lin Nunnery and Wong Tai Sin Temple, HKI - Mid-level elevators, Cat Street (antiques, “antiques” and Mao kitsch - fun to wander), Hong Kong Park aviary - those are a few off the top of my head. Undoubtedly missed something obvious!
Star Ferry is fun and the Ding Ding Tram down the length of HK Island will give you an over view. Kowloon and Hong Kong Island are very walkable - I’ve never felt uncomfortable even by myself. Lots of suggested walking routes on line. Ocean Park and Disneyland if you are into that - Ocean Park is rather enjoyable, it’s has zoo attractions as well as amusement park. Hue Hwa Chinese Department store on Kowloon has traditional Chinese medicine, clothes, furniture, knick knacks. It is different from the multitudinous other shopping mall options which often feature very high end fashion. The indoor shopping is all over HKI and Kowloon, I’m not a shopper, but it would be paradise if I were!
Sounds like you are interested in art - me, too. Sadly, the Art Museum is closed till 2019. I did learn a lot about Chinese pottery thanks to my visits. There is a very nice, chronological exhibit at the Heritage Museum in Sha Tin. A fun little museum of tea and tea pots in HK Park Flagstaff House. I made it to a special exhibit at Hong Kong University and Art Gallery once also, you could check if they are showing anything of interest to you.
I had the most remarkable experience in May hiking on Lantau Island on the mountain near the Big Buddha - it was spring with new bamboo growth, butterflies and new flowers. I felt I was walking thru a Chinese landscape. There are a number of easy to access hiking paths all over the country. The Dragon Back Trail has great views and is not difficult hiking. There are hikes/walks at the Peak that are very accessible for anyone.
The big museums are generally very good. I especially recommend the Hong Kong Museum of History for a good overview of history from pre-history thru turn-over to China and the Heritage Museum for cultural overviews.
Everything is very accessible - I rarely take a taxi, only when I want more speed. MRT and an occasional mini-bus will get you most places. I’ve taken the MRT as late as midnight by myself and never felt unsafe.