Please don't be put off Thailand. I have been several times, and two of those with a young child.
Bangkok has lots for children. There is a great aquarium in the shopping district. The grand palace and main temples are good - 5 year old DD loved Wat Po with the huge reclining Budda! Boat trips along the river are also fun.
We went to Cha-am (near Hua Hin) a couple of hours down the coast as we didn't want to have another flight. There are lots of things to do with children in the area (national parks with waterfalls and caves, water parks, elephants etc).
We have also been to Malaysai - Kuala Lumpar and Penang with 18 month old DD. KL is nice enough for a few days. Penang was really good as there were lots of things to do as half day trips with a child.
Also been to Sri Lanka a few times, once with DD aged 2. I would avoid Colombo as there isn't much to do there, so it probably wouldn't fit into your beach and city break idea! We just had a fortnight on the beach and did day trips. Although if you fly emirates you could maybe have a few nights in Dubai on the way back?
Oh dear, DD is sounding very spoilt with holidays..... We love travelling and SE Asia in particular! Just waiting until 8 month old DS is a little older so we can go back to Thailand. Next year maybe!
I think Singapore and Bali as others say would also be a good option (Only been without children myself though).
If you're not too bothered about the city break then how about Goa? Lots to do with children.