Hi there
Have been a regular visitor to Singapore for shipwatching for since 1993 and there is one hotel venue where you are really able to see a lot. Depends on whether you mainly want to take pics..for which can recommend Kusu Island ... the three shelters at the sea end are a superb location with all passing traffic photo accessible with a decent telephoto lens. Make sure not to miss the last ferry back which normally around 1600 . You will very likely find other shipwatchers there... we regularly meet old friends there and make new ones, particularly from UK, Germany, and Aus.
If spotting is most important then can really recommend the M Hotel in Anson Road, Tanjong Pagar. Get a sea view room and you'll be busy from dawn to dusk. It overlooks the entrance channel to Brani container terminal and pilot boarding ground A & B. Use AIS and from the upper floors (they go to 28 but highest ones over 23 are more expensive club rooms) you can see to the eastern horizon and observe the vessels coming and going into the anchorages as far away as Changi and even off Pasir Gudang. From the lift lobby on the 28th which you'd have to walk up to from 23rd unless a club level guest, you can see large vessels such as VLCCs appearing over the horizon from the east about 25 miles away. For viewing the Western side anchorages , Sinki Fairway berths, Pulau Bukom and other refineries, plus the Jurong container berths, visit Mount Faber viewpoint... best done early in the day or evening so as to minimise heat haze. You can get distant views from there of the Western side of the strait over to Karimun Island, a reasonable but not wonderful view of the LNG and other anchorages at Sultan Shoal, the oil transhipment area in Malaysian waters off Tanjong Pelepas beyond Tuas...though with a lot of clutter and foreground obstructions. There is also a very cluttered distant view to the right of the Jurong and Tuas shipyards where some large vessels can be picked out. To view Sembawang Shipyard go to Sembawang Park on the North of the Island..where you can get a reasonable view of the vessels on the outer berths, and the Pasir Gudang shipyard in the other direction. This is next to military installations so suggest be quick and not pay obvious attention to the military installations as you will be spotted and have to explain yourself... as several I know have had to do. In fact it is illegal to take pics of military items there so steer clear of that.
The area at the West end around Tuas and Jurong is very sensitive and patrolled regularly by the police, usually Ghurka ex soldiers in landrovers. They are armed and will always stop to see what you are doing , and as long as you are not looking at or photographing military installations, they seem quite ok. That area is very big and you need to use a car to drive around. We always get a feeling of discomfort there as though we are misbehaving in some way, but there is a lot to see.
There is no better place to shipwatch than Singapore. If you don't mind the heat it is fine...and the food is just amazing there. Recommend visit Lau Pa Sat hawker centre for cheap and decent food and beer. A further point about the M Hotel... they are used to shipspotters and understand what you are doing. The duty managers there have been there for many years and although not quite understanding why we do it...they do accept it and let you enjoy the views and make you most welcome. There is a bus stop opposite M Hotel whence buses go direct to the Marina Bay ferry terminal for Kusu.
The M is a 4 star hotel , so will not come cheap...but the full day in airconditioned comfort from high up is an advantage to make the cost worthwhile to our group anyway. If you stay in cheap hotels you cannot observe from dawn to dusk as you have no view. Kusu is good but low down and unless you visit in the Festival season which is a few weeks from Oct into Nov each year, you cannot go before 1000 and have to leave by 1600. So far, without going to 5 star and even more expensive high rise hotels, we have found the M is virtually an ideal spotters venue. Another feature to bear in mind is that a good number of vessels arrive from the East, bunker either inside or outside port limits, and sail away East again...never getting closer that about 8 miles from Kusu and too far over the horizon to see. This particularly happens with capesize bulkers.
Hope all this helps... good luck
Ron