A regular school size backpack usually does the trick for daybags.  For girls you may also want to pack an extra small purse for evening outings.  Nothing looks sillier than walking around with a backpack in your evening dinner outfit.

One thing to keep in mind is that your day bag should be as light as possible! You will be carrying the bag whenever you are out of the bus. A bottle of water, light jacket, and room for your camera and sunglasses is all you really need to carry with you. 

Make sure to bring a combination lock to lock your main compartments to keep pick pockets away!  Also, in extreme cases, if you’re in a large crowd and really don’t feel safe with your valuables hanging behind you, you can always wear your bag in the front.  You may look like a kangaroo, but at least you know no one will cut the bag while you’re distracted.