On my way to Australia I have a very long stopover in SIN (from 0720 to 2350), and I'm considering taking a day trip to Kuala Lumpur or Jakarta. I know it's quite crazy, but I guess it's typical me: in the past I've spent my stopovers taking a ferry to Batam and back, gone to Johor Bahru or simply explored Singapore.

I have a few questions:
- Even if I'm actually in transit and already have the boarding pass, I guess I must go through Singapore immigration so as to officially enter the country I'll be leaving shortly, right?
- I've seen that Tiger Airways, Air Asia and JetStar are flying these routes. Should I avoid any of them? (For such a short trip I'd rather use a low-cost carrier, I don't want to spend too much).
- I've chosen KUL and CGK because, even if I've already been to Malaysia and Indonesia, I've never visited their capital cities. But I know that I won't be able to see much. What other places can you recommend? No more than 1.5 hours away; there must be plenty of flights serving SIN and the other city daily, so that I can choose other options in case my booked return flight is delayed or whatever; And it has to be a country that's easy to enter for a European citizen (visa on arrival as in Indonesia is fine). Your suggestions are more than welcome.

Thanks in advance!