There are many things to do here, as with most Moroccan cities it is enough just to wander around and adventure where something takes your fancy.
In the Kasbah (Oudaia) there is an amazing cafe that looks over the sea, where you can drink mint tea and eat sugary treats. The staff are very friendly and you can stay as long as you like soaking up the atmosphere.
There is also a large and tranquil park next to the Hotel Sofitel, where people run and play football etc. You can also use the pool at the Sofitel for a charge. The park is a 10-15 Dirham taxi ride (10 minutes) from la gare central.
Theatre Mohammed V Theatre in Downtown Rabat, nothing absolutely outstanding but there are performances each month.
Jazz au Chellah is a jazz festival organized each year in june by the ministry of culture, the city and the european delegation. The website might have some issues.
Mawazine is a festival of world music that takes place annually in Rabat featuring Arab, African and international music icons during May. It is controversial as some of the country's Muslim politicians have criticised the event for "encouraging immoral behaviour". Artists such as Stevie Wonder, Carlos Santana, Elton John or B.B. King have performed at Mawazine. There are various scenes around the city.
Amnesia 18, Rue Monastir, Downtown Rabat. If you like clubbing then dress up, this is the hippest club in Rabat.
Royal Golf Dar Es Salam The domain is spread over 440 hectares of trees, flowers, and water. If you have enough money, a car and are desperately looking for a quiet area to walk around or to play golf you will like it.