The title is about batteries, but the subject of using cheap phone chargers has come up.
Small note: Whenever I refer to "the regulator" below, I'm talking about the onboard regulator of the arduino variant you are using, not to any regulator chips inside the phone charger. Just to be very clear.
Safety:
If you ARE going to use cheap phone chargers, at least buy several and crack one open to look at the isolation on the PCB. (look at the pics on some web sites that have done this to get an idea what you are looking for) Then always unplug it before working on the sensor node - use an alternate high quality supply while programming and testing, Just In Case. And don't have any exposed conductors on your finished node, that could be touched.
I would avoid the most compact ones with little room inside the case.
And you might want to test the temperature of the charger under load before deciding to use a given model.
Power quality.
At least measure the output with a voltmeter, under the loads you use.
If you try to run a 5V arduino (eg: APM = Arduino Pro Micro) from a 5V charger you could have problems (you must test). If you use Vin, you will likely have problems because there isn't enough voltage differential for regulation, a condition known as dropping out of regulation or drop-out. There are regulators with low drop out (LDO) specs that require less difference between input and output voltage, but those specs vary depending on the regulator and load. The ATMega chips have a lot of slack, so a 16 Mhz chip will probably still run fine if the output of the regulator is, say, 4.5v or maybe 4.0 volts so the voltage drop may not be critical. But the regulator may not be keeping the supply as stable when in drop-out - varying the voltage as load changes or passing through variations in the supply voltage (coming from a cheap charger).
So you may be tempted to just feed the charger 5v into the arduino's VCC=5V pin. That may work, but (1) some regulators don't like having power applied to their output pin only, so check that it doesn't overheat or remove it, and (2) the regulation on cheap chargers can sometimes be very bad - either off-voltage or with a lot of ripple and noise. Some are better than others. Expect the cheap ones to usually get flakey in these regards well under their nominal supply (eg: a charger which says 1A might work well only up to half that). And they may be poor even at low current. If you have a scope you can look at it (being careful about isolation and safety).
If you have a 3.3v arduino, you can probably feed the charger's 5v signal into its Vin and get a reasonably well regulated VCC=3.3v.
WIth the above qualifiers, some cheap chargers work fine in the right situation.
Of course, you should instead get a high quality power supply for each node. One problem is knowing that it is indeed a high quality supply - just paying more isn't a perfect predictor of that. Using a name brand may help, but there are plenty of reports of problems with name brand suppies too (tho we hope they are statistically less common). And a good supply may sometimes cost more than the node (3.3v APM = $3.50, nRF24L01+ = $1, dht-11 = $1, power supply = $10?)
