There are a ton of choices out there for a city commuter bike. Practically any of the 500cc or less UJM's (Universal Japanese Motorcycles) from the 70's and 80's will make a good choice, and get excellent gas mileage ~ 70MPG.
Now riding gear is more important than the motorcycle, don't skimp on it, even if you plan on only going around the block. For a leather jacket, DO NOT wear a fashion leather jacket, only wear a motorcycle jacket. They are made from thicker tougher leather and are cut and sewn differently for more comfort on the bike. Also try to buy one that has CE certified armour on the elbows, shoulders and back (also the chest if you can find one). A cheaper solution would be to buy a textile based jacket, they are not as good but are cheaper, do not buy a mesh jacket. I also suggest you buy a full face helmet, the open face or half helmets only protect the area covered. You would look pretty funny after getting in an accident and having you jaw torn off. Riding pants are just as important, your knee will probably be the first thing to hit the ground in an accident. Regular denim jeans are not good enough, at the minimum I would suggest you buy a pair of Draggin Jeans (google it) with the armour knee pads. If you can buy some leather pants or chaps that is much better protection.
Also if it is available in your area I would sign up for a MSF course (Motorcycle Safety Foundation). You will learn a lot, they will teach you all the basics you will need to survive on the rode. It doesn't make you an expert, but provides you with the basic skills and knowledge to practice on your own. Also you may get an insurance discount and a discount on gear at your local shop.
And the most important thing I can tell you: DO NOT RIDE WITH SQUIDS. Squids are the guys you see wearing shorts, t-shirts, flip-flops doing wheelies or stoppies or going 100+ mph on the highway on a supersport bike. Do not even talk to these guys, their stupidity is contagious and will kill you.
But the 250 ninja is an excellent choice for a city commuter. It is light, cheap, and highly maneuverable.