Mario Kart DS a racing game that alows you to race in the grand prix and do time trials and see if your time is close to the time of NoA employees and even try to beat there time or Animal Crossing:Wild World,where you can live your life pay off your morgatge for a house go fishing and even connect with your friends towns online with Nintendo Wifi Connection
Your DS will not last that long, so if you have a second battery you might want to take that and a screwdriver.
As for games, Pokemon Black/White is really good for long periods of time. Other than that, idk, I don't play a lot of normal DS games. 3DS is where it's at lol