HK resident here.
If you can get a deal, consider the Upper House at Admiralty. Very nice- top pick for "staycations" amongst HK'ers. Even if you dont stay there, go for a drink at Cafe Gray, the bar on the 63rd floor- amazing views.
Peak tram- best bet is to either hike up or get a taxi/ bus (15 from exchange square or minibus 1 from IFC) and get the tram back down as the queues tend to be shorter. The hike around Lugard Road offers good views. If the cloud's low, dont bother as it's just foggy and damp and miserable up there.
Beaches- kind of depends where you're going next. If going to Thailand or somewhere, dont bother. They're nice enough but you'll get better in SE Asia/ Australia. Best beaches on the island are probably Shek O and Big Wave. However, the water can be not that clean if I'm honest, depending on the tides. If you like hiking, there is some amazing trail. I can recommend depending on experience and how long you want to go for/ how much you like big hills. If you go to the Big Buddha you can hike up Lantau Peak from there, which on a clear day will give you amazing views from 900m+
I'm a bit meh about Lamma. It's ok and there's a pleasant 4k hike from one side to the other, but hard to miss the mahooosive power station stuck on top of it.
You might like the Chi Lin nunnery at Diamond Hill MTR- beautiful gardens and very zen. There's a nice little veggie restaurant there as well. Closer to diamond hill there are tonnes of fortune tellers but you need to take a translator as they dont speak English.
Best markets are on Kowloon side. Re fakes, yes, they're everywhere and they're good but be aware that you're basically indirectly funding all sorts of bad shit if you buy them. The ones in the markets are ok- it's the ones where you get taken into secret shops and pay, say 33% of the normal price that are triad ops.
Theme Parks- if you like them Ocean park is better than Disney for adults. Get your tickets in advance and get there for opening.