If you are worried about mosquito bites because of malaria risk, then 50% DEET is what you need. It is unpleasant stuff, but then again so is malaria. You need to apply it on any exposed skin and rub it in well. It will mess up your nail polish and other stuff it touches. If it’s just because you don’t want to end up with itchy bites and are not bothered about the disease side of things then anything you like the smell of will dissuade the majority of mozzies. Doesn’t really matter if you buy it here or there. Singapore is not a cheap place, so not much saving to be made on buying it out there, having said that I rarely use mozzie spray in Singapore, perhaps only in the gardens or walking the McCritchie Trail.
In terms of what to see, both Singapore and Bangkok have loads to see and do. I am more familiar with Singapore and have been lots, but am always happy to go back again as I haven’t seen or done everything in the 9 years I’ve been going there with work, so it’s worth having a plan for your 2 days there!
My highlights include: Gardens by the Bay - a walk between the Supertrees, the light and sound show, the rainforest house, and a snack at Satay by the Bay. Then walk back through the Marina Bay Sands and have a cocktail in the bar at the top. A boat ride round the harbour, seeing the Merlion, then get off and have dinner at Clarke Quay, or if you have not had enough satay yet go to Lau Pa Sat. If you are jet lagged and not ready for bed, there is a great nightclubbing scene or if that’s not your thing go to the Night Zoo, which is just brilliant. You get to see all of the animals that are active at night, and there are some great displays. The other big day out my family enjoy is to Sentosa Island. Very easy to get to by metro, but you can also go by cable car if you want. Once there there is Universal Studios, a water park, giant zip wires, the aquarium (which is stunning,) beaches, various WW2 historic sites, the Trick Eye museum (which is hilarious if you like taking selfies or optical illusions, make sure you have plenty of charge on your phone.) You can go into China Town and queue up to eat at the Michelin starred street food hawker’s stall, walk the historic trail through town, see the Battle Box, hike through the rainforest at Macritchie Reservoir, or just hang out in a really beautiful city. 2 days will definitely not be enough!
For Bangkok others will be better placed to comment, but the Grand Palace, Wat Arun and Wat Pho are the big sights. If you plan to go into any temple or palace be aware that you much have shoulders and knees covered - if you forget there are opportunistic locals selling tie dyed and printed ‘palace pants’ and scarves outside the places so if you always wanted an expensive pair of wafty trousers printed with elephants, this is your chance! A long tail boat ride into the klongs is brilliant too, you’ll start out on the river but make sure they take you down the side canals as this is where the most interest is. Keep your eyes open for huge monitor lizards, they are everywhere - I once saw one chasing a squirrel down the pavement there! The food is a main attraction in itself in Bangkok. My work colleagues tend to head out clubbing after dinner, but I go for a Thai massage. There are massage parlours everywhere, staffed by small but fierce and strong women. Get a recommendation from your hotel concierge if you are worried about ending up in the ‘wrong sort!’ I quite often have a massage a day when I’m in Bangkok.
Koh Samai - never been, so can’t help there.