This is an interesting question because "technology" is such a limited concept and it depends so much on the cultural and social structure surrounding it. You could bring a working steam engine to the Roman Empire, but it wouldn't matter because the various forces which encouraged industrialization in Europe in the 1700s and 1800s would be absent. You'd have to change the political, social, and intellectual structure of Rome before a steam engine would be more than a toy. I mean, the Chinese were like 600 years ahead of the Europeans on industrialization, but it declined because of social forces.
So with that in mind, I'd take a powerful microscope back to the Persian empire, to show it to Cyrus the Great. With somewhere around half the world's population in Persian borders (in terms of world population share, the largest empire in history) and a relatively cohesive and effective imperial government, I could prove the germ theory of disease and have it become widely accepted 2300 years early. As long as people knew that there were little bitty animals that lived in the air and food, and some of them made you sick, then human civilization takes a gigantic step forward.
That doesn't necessarily mean that everything will get solved - knowing that pathogens cause illness and knowing that fleas borne by rats cause the bubonic plague are two very separate things. But if people just wash their hands more, and if they tried surgery with just the most basic sanitary procedures, then that's a gigantic leap forward. It also sets the ground for further discoveries of things like antibiotics.
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