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It's difficult to do justice to places like Singapore & Bangkok on a day trip basis. Additional thoughts for Singapore, Raffles Hotel for the Origional Singapore Sling, Clarke Quay/Boat Quay, or as stated previously Orchard Road for shopping & try the Food Court on the bottom floor for lunch. Bangkok, a boat ride up the Chao Phrayo River to see the Golden Temple or Paht Phong for the cheapy markets & the type of 'Night Life' Bangkok is famous for. The 'Floating Market' which is always pictured in Bangkok travel brochures is quite a way out of town & needs a least half a day to fit it in. Hope this helps. Looks like a great cruise.
I haven't actually done the trip but I have lived in Singapore and can highly recommend the zoo, if you like animals that is, I can also recommend Sentosa Island, China Town and Orchard Road for shopping and the Cuppage Centre for eating. Have a great time, Singapore is a delight as are the people who live there.
Forgot to mention the MRT which is Singapore's amazing transport system, it's very easy to use and you will be able to get to almost anywhere on the island very cheaply so no need to pay for expensive excursions, cabs are also readily available and reasonably priced. As Wilba so rightly says it is difficult to do it justice in a day and his suggestion to have a sling in Raffles is an excellent idea, Raffles is an institution in Singapore and a "must do" while you are there.
I suggest you check out this site which gives you all the info and tips of what to do in each PORT that you will CALL at. Look where the name should be.
Also in Singapore, if you take the tip of a Sling in the long bar at Raffles, the Raffles City Shopping mall is right next door and will save you time( and a very hot walk!!!) to Orchard Road. Also for the most fantastic views of Singapore harbour the islands and Indonesia, go to the Stamford Hotel (again just around the corner from Raffles) which is the tallest hotel in Asia and visit the bar on the 70th floor. Fabulous at nightfall when all the lights start to come on all around. We did a New Zealand and Australia cruise earlier this year and loved it. If you have the opportunity, do go to the Opera in Sydney( I mean to a performance, not just the tour of the Opera house) Also a float plane flight-seeing of Sydney is pretty memorable. We did one where we were flown all around the Harbour then out to a River side restaurant for a superb lunch , then the flight back to Sydney. It was pricey but memorable---my Husband refers to it as our "Nicole Kidman moment" disembarking from our private plane at the restaurant jetty!!!In New Zealand the Te Papa museum in Wellington is brilliant. We also saw around the Parliament Building but opening there of course depends on whether Parliament is sitting. If you can get in to see it, its a worthwhile visit. Finally we loved the train journey through the Southern Alps, with pretty spectacular scenery. Its a full day shorex with lunch on the train Have a wonderful time. Cynthia.
Now I was not aware of Stamford Hotel but have noted it for my next Singapore in May. Thanks.