I'm installing an outdoor outlet on the side of the house and also need to be able to power an outdoor island on the other side of the patio. The cleanest way to get there is to cable around the patio, but was unsure of how far away from the patio the trench I build needs to be. Are there any rules on how far a trench needs to be from the house/patio?

No rules about distance, the cable in trench can be directly adjacent to the patio or house.

The requirement to be concerned with is depth.

If the circuit is no more than 20 amps 120 volts and has a GFI circuit breaker protecting the circuit direct burial cable can be 12 inches. Otherwise the cable will need to be 24 in deep.

Thanks! Confirmed with my city on the depth requirements.