Where to connect unused 555 timer ICs pins?
As Marcus comments: just follow the datasheet or the schematic drawn up by someone else.

There is no general rule concerning pins you do not want to use as it depends on the function of the pin.

In the 555's datasheet we see (on page one) that the discharge pin is connected to the collector of an NPN to ground. There is no harm to leave it unconnected. Connecting the discharge pin to ground is also OK, that would simply short Collector and Emitter and would make no difference to the rest of the 555's circuit.

Generally input pins need to have a properly defined voltage so the TRIG pin should never be floating as that can result in unexpected behavior.

The "CONT" is also an input but if it is left floating then there is an internal resistor divider which sets the voltage of the CONT pin (at 2/3 of Vcc). So the CONT pin can be left floating if needed. Often a capacitor to ground is connected to it to make that internal voltage more stable. You could also connect the CONT pin to some other voltage or a variable resistor to influence the voltage on the CONT pin. Some 555 circuits use this in some way.

So: it is perfectly fine to leave a pin unconnected if the circuit needs that.