Sacman:
I am pretty sure you are going to have a problem using a simple 3.3V regulator with a 3.7 lipo.Dropout voltage on a typical 3.3V regulator is going to be a little bit over 4V. So if you fully charge a Lipo and pump it through a standard 3.3V regulator you are going to have a very short life cycle if at all. I don't remember the exact number but at 4.2V, your regulator might be supplying less than 3.3V right out of the gate and it will fall off rapidly from there.
Even a Low Dropout Voltage Regulator is going to struggle in this case since your operating voltage is so close to the maximum voltage of the battery.
What you need is a Boost Convertor that will regulate your 3.3V down to less than 1V.
Here is one from Sparkfun that would work perfectly for what you are trying to do:
LiPower - Boost Converter - PRT-10255 - SparkFun Electronics
This one is even better since it has a a charge circuit built in as well and is only about $5 more.
https://www.sparkfun.com/products/11231
If you already know all of this then I apologize.
I'm actually using one of these (although time will tell if I will be able to successfully solder it).