10 kΩ is a typical value for a pullup/pulldown, and the 500 µA loss at 5 V is usually not a problem; the optocoupler's LED will usually need a multiple of that. For low power applications you can increase the value, and the upper limit is determined by the 74HC244's input leakage current. The datasheet says that is maximum 1 µA, then a 1 MΩ resistor may cause a 1 V drop across it. That's a rather large value, still OK at 5 V supply voltage, but I would choose a lower value.
A 100 kΩ resistor will cause a 50 µA leakage from the device's output, and a maximum input voltage of 100 mV when floating. This looks like a good solution.
Typically, the pull down resistors for CMOS logic are between 10kΩ and 100kΩ, up to 1MΩ for battery powered devices with low power consumption.
At the same time, the LED in the optocoupler is a current-driven device, as opposed to a voltage-driven device. If an LED is connected to high impedance, it will not produce light. Effectively, an LED works as a pull-down by itself.
If it's a CMOS circuit, use 100K. It will draw 10 microamperes per volt, draining any stray capacitance reasonably fast. With a higher amount or resistance, you might experience problems in dry weather, when there are strong electrostatic fields. If power consumption is not an issue, you can use less resistance, such as 10K.