The ESP32 uses perhaps 10 or 20 mA while connected to the network. For hobby projects, it's a good choice.
While disconnected, it is supposed to be able to sleep at a few uA (but seems to get down to 100 uA or so).
The libraries are still a work in progress, and some of the peripherals are beta-quality (the ADC is pretty awful, for example), but the WiFi part of it works pretty well.
I've not used the particular MCU, but I find TI's products quite well designed, with a learning curve. You could look into the CC3200. It claims about 1 mA while connected and sleeping. (I've used their CC2650 BLE module and various other MCUs).
Note that both of the above are MCUs with integrated wifi stacks. There are also some external Wifi peripherals (like how ESP8266 is often used), but I don't have experience with them.