I highly recommend taking a river cruise in Singapore. Better if you do it on the first day. You get a nice overview of the city and just a kick-back time listening to the narration. It was $25 (US) and worth it. No need to book in advance, we had no trouble booking it right on the day that we wanted and no lines. (Maybe we were lucky.)
Here are a couple of panoramas that I took of the city as we waited for our cruise.
After the cruise, we went to the top of the Marine Bay Sands Observation Deck. Yes, there is an admission. My memory is it was about $17 US. You may think this is pricey for just a view, but you just have to do it. There's something about being able to see practically the whole city from atop. You get a good orientation to the city and it is just a pleasant way to spend the time. They will not let you swim in the infinity pool if you are not a guest, so either book a room there, or forget about it. The pictures don't really convey the fun, but it was.
I have traveled quite a bit, and am using this page to record some memories. Travel is a wonderful education, expanding your view of the world, of other cultures, of the beauty of diversity.