The stations you need are : Singapore (Woodlands) to Kuala Lumpur (KL Sentral – Sentral Kuala Lumpur)
For information on things to do in both Kuala Lumpur and Singapore visit there tourism websites it gives a good idea of all the things to see and do, and not just the tourist things.
Some of the things I plan to do or look at in Kuala Lumpur is see and try and get a ticket to up the petronas twin towers the price is around £14 but sells out fast! There is also the botanical gardens what is free of course and there's a hotel opposite the towers with a sky bar and pool what I'd like to go to on a night to get an amazing night time city view with the towers. Another thing to see is the batu caves!
In Singapore the things I want to see are all mainly free as it the architecture around the Bay Area as there is lots of are and sculpture too. One thing I do want to see and do is go on the flyer (on the bay again) it's just like the London eye but in Singapore it costs around £13 and then you get a lovely view of the city. The Bay Area is the marina area and has lots of things to see and do.