To avoid an address conflict, I need to connect an SHT31's address pin to high. The datasheet, doesn't specify if I need any resistors for this or if it has to go directly to VDD. I'm concerned about power consumption since it is a battery powered device. Is it ok to connect it directly and if not, what value of resistor must be used to obtain the high address while consuming little power?
Since the datasheet does not specify any requirement, it can be directly connected to VDD.
So a resistor is not necessary. However, nothing prevents putting a resistor to pull the pin up. It does not make much difference, as long as the resistor has a reasonable value, like between 0 ohms and 100 kohms.
Using a resistor to pull up the pin, will make the pull-up weaker (both adding the resistor and the need of longer traces) and the pin will be vulnerable to noise (for example if a antenna radiates nearby, it will disrupt the pull up, and it may cause the pin to read 0 instead of 1).
And yes, it will draw a little bit of current, but usually the pin is already some Mohms of input impedance, so a little current is drawn anyway.
So you have to trade between power consumption (if you do not add a resistor) and noise tolerance, higher price, less space (if you add a resistor)
If your IC has this option, pull down the pin instead of High. It will solve all the above issues.