A Teensy 3.5 might be better. More pins than a Nano and it has an SD card slot which doesn't share pins with the header pins.
It is 5v "tolerant" which means that it can accept 5v digital inputs but analog inputs over 3.3v will read 1023 and digital outputs will only go up to 3.3v
Or maybe a Teensy 2 has enough pins for what you need?