why not? try, you may get lucky and they let you enter the Riyadh's Prince Majlis or where he meet his visitors, but dont think much of 1001 nights, there are no Harem girls.
The Al-Thumairi Gate, in the centre of town, is an impressive restoration of one of the 9 gates which used to lead into the city before the wall was torn down in 1950.
It is a massive tower containing a shopping cnter , a four seasons hotel , luxury restaurants and more.
A fine example of the odder examples of modern architecture you will find in the Gulf. The design is meant to evoke the traditional Bedouin tent.