The old city inside the murallas is amazing, and the people are friendly. There isn't much to worry about here beside the street vendors who are numerous and _extremely_ persistent. Everyone wants to sell you something. There are many internet cafes (1500 - 2000 pesos for an hour) and tons of places to change money, too.
Do not change money with the guys on the street, if the stories are to be believed (I believe them).
I bought a pre-paid cellular for convenience. It is rather expensive to use it, 800 pesos a minute.
There are plenty of day excursions - Islas Rosario, Castillo San Felipe, La Popa, etc...
If you want to stay in the old city, instead of the new Miami-Beach style Boca Grande area, I recommend hotel Tres Banderas in the San Diego district. It is nice, and the staff are friendly. Some other hotels in the old city are.... disgusting.