November to March is by far the best time, with warm, dry days, cool evenings and comfortable weather for the corniche, beaches and outdoor sights. Spring and autumn shoulders are workable but warming, while May to September brings extreme heat and high humidity that pushes almost all activity indoors or to after dark.
Summer in the Eastern Province is genuinely extreme, with temperatures often above 45 degrees Celsius and heavy Gulf humidity that makes it feel hotter. From late spring to early autumn, stay hydrated, avoid the midday sun, use air-conditioned malls and museums, and save the corniche and beaches for the evening.
Saudi Arabia is welcoming to visitors but socially conservative. Modest clothing that covers shoulders and knees is respectful for everyone, women no longer need an abaya but should dress modestly, public displays of affection are best avoided, and it is courteous to be discreet around prayer times when some shops briefly close.
Getting around means a lot of car travel on fast, wide roads where driving can be assertive and pedestrian crossings are limited. Take care as a pedestrian, use marked crossings, wear seatbelts, and if you drive, watch for sudden lane changes and high speeds on the highways between the cities.