At RUH, stay airside—modern terminals and lounges are better than dealing with long security processes.
Take Metro Line 3 from RUH Airport Station to Riyadh Front Station in about 25 minutes (SAR 4 / $1.10). Riyadh Front is a large, modern outdoor mall and dining complex with multiple restaurant options. It is air-conditioned and walkable, making it a practical stop for a tight layover. Return the same way. Budget 2 hours in Riyadh Front and allow 60 minutes for total transit time.
Diriyah (Al-Turaif District, UNESCO) is the mud-brick historic capital of the Al-Saud dynasty. It is 30 minutes south of Riyadh city center by taxi (SAR 40 to 60 / $11 to $16 from Metro terminus). Entry to Al-Turaif ranges from SAR 75 to 95 ($20 to $25). Allow 2 to 3 hours at Diriyah. The Kingdom Centre Tower (observation deck SAR 85 / $23) and Olaya Street area are also within 30 minutes of the metro network.
The Edge of the World (Jebel Fihrayn) is a 90-minute drive northwest of Riyadh. The dramatic 300-meter cliff drops to the ancient sea floor and offers wide desert panoramas. Organized half-day tours depart from the city from SAR 150 to 250 ($40 to $67) including transport. Book in advance. Combine with a Diriyah visit in the afternoon for a full 10-plus hour day.