I've used these...
http://www.ladyada.net/make/mintyboost/
...to power projects. I don't like the way the SparkFun one behaves when the battery is close to the end of life but both work well. I suspect the Minty Boost is a bit more efficient but I haven't had time to test.
Floating inputs drain power like PacMan eats dots. Unused pins need to be configured as INPUTS with a PULLUP or PULLDOWN resistor or they need to be configured as OUTPUTS set LOW. If you do nothing, it's very likely the pins will float.
- Brian