Daily the tires should be checked for correct pressure, oils and lubricants should be checked that they are at their proper levels. Things like wire rope and safety chains should be examined for damage or wear that might make them unsafe to use.
Maintaining equipment stowed on the tow truck is also very important. For example, the snatch block requires regular attention with regards to lubrication and proper storage. It is never a good idea to leave the snatch block out in the open where it might get wet as rust and stagnant water diminish this tool.
Keeping the truck fueled is always going to remain a priority because of course without fuel, work can't get done. Something else to consider is that even though the truck is going to get low on fuel, you should try to not let the tow truck get under a quarter of a tank as a means of a reserve just in case a law enforcement call occurs. Not letting the truck get too low on fuel also prevents sediment in the fuel tank from getting introduced into the filter and intake components. Choosing good locations to get fuel from is another thing to keep in mind. Older facilities can have older pumps and underground storage tanks that can transfer sediment into the tow truck.
Tow trucks can be run for hours at a time and suffer far more punishment than typical vehicles, so proper care is essential to get the most out of the vehicle as possible.