That's because there's nothing to see. I certainly agree with you that you should take the opportunity to explore KSA if you have the chance. I've spent a bit of time in Riyadh and can't recommend anything specific -- I would just wander around and see the somewhat different (by Western standards) aspects of daily life. There are the modern amenities like Kingdom and Faisaliyah towers and the shopping malls to which they are connected, which are a bit interesting for their local quirks, but I would prefer to see the street life, such as it is, and have a tea at a local cafe or two.

Even worse on Friday. There is utterly nothing open until mid-afternoon. Though Saturday is a work day so you should see life as normal.

The Four Seasons is at the level you would expect and has a nice pool area, or the Rosewood hotel seems interesting (I've been but never stayed). Both are well-located. All of the major chains (InterContinental, Marriott, Sheraton, Radisson Blu) are there but a bit ordinary -- generally dated properties with uninspired amenities. The InterCon has a nine-hole golf course.

Sorry I can't help more. Perhaps a local could at least give you recommendations for a restaurant or specific neighborhood to check.