Bali is great, my big favorite, but quite far, even with a stopover in HK. I would say Caribbean. I have done Jamaica, Santo Domingo, Curaçao and Isla Margherita with my DC. Curaçao is not so typically nice but the safest for water, food, ..., Santo DOmingo is gorgeous but with Cholera in Haiti, I wouldn't go. Maldives is fantastic, but stay on a big island, you don't want a doctor to be too far away It may rain in Rome for a whole week in february.
I have taken a small baby to the Far East before and it was fine. However do seriously consider SA. We travel all over the world regularly with kids in tow. The small time differnce therefore no jet lag is not to be sneezed at.