Since you might be open to flying then another nearby option to consider is Siem Reap in Cambodia. It’s a pleasant tourist town on its own, but it only exists as the gateway to the amazing Angkor Wat temples nearby. Those temples are by far the most dramatic and memorable tourist attraction in southeast Asia, and I think your daughters are old enough to appreciate it all. But again, the town of Siem Reap is nice with plenty of other things to do, so it’s a great all around stop.
Southeast Asia is easier to deal with, and there are cheap flights connecting in the Middle East and landing in Bangkok, Kuala Lumpur, and Singapore. Each of those is a very interesting city, and there are many smaller places to go in the same region. In Malaysia there is Penang and Melaka. In Thailand there is Chiang Mai and quite a few others in that area. In Laos you can visit Luang Prabang, which sounds like it could be a winner for you. And there is also Siem Reap, which is home to the amazing Angkor Wat temple complex.