Momo
I'm tempted to say the best thing to do in Riyadh is go back to the airport and leave, but that would not be entirely fair.
I have stayed at this property and it is a decent enough place (the Radisson was fully booked, so I took this as an alternative), located at the end of Olaya Street.
Normally it is quite safe to walk up Olaya St to the Al Faisaliah mall (about 10-15 mins, take care as you have to cross the main drag.)
You can pass by the computer market and buy any pirate software CD for 10SAR (about 2.65CHF) or just have a browse around - sometimes you can get a decent deal on equipment, but haggle ;-)
The Faisaliah mall has a foodcourt upstairs, with some decent fast food options (Aladdin, if you like Indian, is good IMHO and inexpensive.)
Other things to do, take a taxi to the Kingdom Centre and pay to go up to the top, viewing Riyadh from high is interesting; they also have a mall underneath.
If you like Japanese, the Shogun restaurant at the Radisson is excellent, if a little costly.
Of course, do check with reception as to whether it is okay to walk about; Riyadh is normally safe, but with the current unrest in North Africa and Bahrain, things could change quickly.
Despite the bad press that the Saudis get in the west, I've found most people in this part of Riyadh (which is upmarket) to be polite and courteous to foreigners and your encounters in malls etc will be mainly with asians (Pakistanis and Philipinos) who are also generally pleasant.
Enjoy the trip.
A small tip, the only transportation from the airport to the hotel will be by taxi and the airport taxi drivers can be a little difficult, so if you have to get a taxi there, try to choose a pakistani driver.
But preferably pre-order a transfer through your hotel. Expect to pay around 120SAR, but you should be in a Toyota Camry or similar, with comfort and air con.