USB charging and powering circuit with MAX1555 and MAX1881
The MAX 8881 EUT33 is a LDO in the first place. Note that the battery voltage maximum is 4.2 Volts when charging - which is too high for many 3.3 V circuits - so you need a voltage regulator in most cases anyway.

The part is SOT23-6 and $0.86 @ 1k (from Maxims website), so both small and cheap.