Arduino nano as Part of another circuit
You can find the full schematic for most arduino boards by googling "arduino board name schematic". For the most part, a bare bones arduino is just a Atmel microcontroller, a capacitor or two, a few resistors and a voltage source. Then you add things like an external crystal for a better clock, a serial to usb adapter, a voltage regulator, etc as needed. Now you can get a microcontroller that has the usb to serial part built in really. And plenty of places sell just the pre-programmed microcontroller for you.

As the cost of the microcontroller is like a few dollars at best, you might as well stick with a ATmega with more pins, instead of going with the smaller, cheaper, but weaker ATtiny cousins.