Generator Light Replaced battery and light did not come on. The next day it came after traveling for about 30 minutes. What else should we check? Battery cables, alternator, belts, etc.

Check heavy gage wire on the back of the alternator for B+ voltage ?
When the engine is running, the generator turn on signal is sent to the generator from the PCM, turning on the regulator. PCM - engine computer . Take the vehicle to a qualified repair shop an have it checked for DTC'S
DTC B1327
DTC B1513
DTC B1514
DTC P0560
DTC P0620

The PCM monitors the system voltage to make sure that the voltage stays within the proper range. Damage to components, and incorrect data input can occur when the voltage is out of range. The PCM monitors the system voltage over an extended length of time. If the PCM detects a system voltage outside an expected range for the calibrated length of time, DTC P0560 will set.
Action Taken When the DTC Sets
• The PCM will not illuminate the Malfunction Indicator Lamp (MIL).

The battery light means the alternator is not charging the battery. The charging system would need to be checked out when the light is on.

Have you fuel? Filter may be blocked or ignition coil breaking down?

You should first fill the transmission fluid to the correct with genuine Nissan Matic J Transmission fluid and replacing the transmission input shaft speed sensor. Its costs approximately $113 at the dealer for the sensor.

A flashing AC light is usually a sign of a slipping belt which is almost always caused by a worn belt tensioner

take it to an accredited auto electrician for a charging system check including the voltage regulator and wiring conditin
at idle the battery voltage will be 12-13 volts and at 2000 rpms it should be steady at 14.5-14.8 volts dc

usaully when battery light is on it is your alternator is not charging you can have it checked at a parts store for free or go to walmart tle and ask for your charging system to be checked not just your battery

I'm not sure where you got your alternator tested, but recently I was in the same situation with my 1998 avenger and the alternator was at fault

check dome light, glove box light, trunk light. anything that might have power to it all the time.
Greg