Travelon has bags designed to be worn cross-body in a variety of fabrics/leather, and Buxton has a similar version in leather. Baggelini also has several similar styles, but I've found them to be a bit more expensive.
There are certain things I have to carry: contact lens solution, reading glasses (yeah, my contacts require reading glasses these days!), sunglasses, tissues, etc. A cell phone is a requirement this trip, as we have several people going in different directions--and some serious illnesses at home that will necessitate telephone calls at inconvenient times. I use a credit or debit card only for emergencies--and vacation doesn't count as one in my life!--so I also need to accommodate cash/travelers cheques.
I carry a standard leather shoulder bag that is about 10" wide by 7" tall and about 2.5" deep. The shoulder strap is adjustable so I can use it cross-body if necessary. Anything unnecessary for the trip is removed before leaving home; anything unnecessary for the day's activities is left in the hotel room.