The square itself is pretty busy and touristy, but if you stroll around you’ll find nice places for a coffee, lunch or dinner.
Go for example to De Balie. This is a vibrant cultural center with a beautiful Grand Café. (Kleine-Gartmanplantsoen 10).
From Leidseplein it is also a short walk to the city theatre Stadsschouwburg and famous music venues like Melkweg and Paradiso.