If you intend to go to both Bali and Langkawi, your best "base" would be KUL. AirAsia flies to both Denpasar and Langkawi non-stop for next-to-nothing ($20-30 each way). Getting to KUL is tricky, however. Another poster's suggestion about TG non-stop NYC-BKK would be ideal. BKK-KUL is a quick and cheap ride on AirAsia or an easy add-on to your TG ticket.
Your alternative is to base in SIN. Flights to DPS and LGK are not cheap from here (no LCC alternative) but it's very convenient as SQ has boatloads of flights from North America to SIN. Wherever you decide to base, you'll have to do multiple round-trips to get to both islands as they are located on opposite ends of South-East Asia. I wholeheartedly second the suggestion to use the SQ/TG non-stops as they have premium economy classes. They do cost more than normal economy classes, however. If you intend to use miles to upgrade, you'll be "stuck" on NW (or UA). They both fly to BKK and SIN so that's an easy choice.