Designing small size AC/DC to provide 3.3 V for MCU
Your need for \$200\:\textrm{mA}\$ does place a special burden. This means getting near a full watt of power. Monolithic Power's MP103 might have been an option, if you were looking for a little less current compliance. But it doesn't get even to half of what you are looking for.

Please do take a complete look at the EE.SE link for a question I asked, earlier this year. There are some interesting possibilities from that. One of them was an enclosed AC DC Converter providing \$5\:\textrm{V}\$ and up to \$800\:\textrm{mA}\$ from a VAC input up to \$264\:\textrm{V}_\textrm{AC}\$. The Digikey link to a \$3.3\:\textrm{V}\$ rated unit from the same manufacturer is here and also here. Either provides more current compliance than you need. And neither is exactly cheap. But the more expensive one is for household use and has all those nice ratings and approvals you may want. May be worth the extra to you. The other module also looks nice. (My EE.SE question has additional thoughts, though. So peruse it and see what you think.)