To begin with, it would be a good idea to delete your duplicate Threads on this topic so that you keep all replies in the same place.
"the train stations and major attractions are full of teenage gangs and pickpockets."
It would be interesting to know where you read that, as (IMO) it provides an exaggerated view of the reality. There will be pickpockets around, especially in more crowded locations such as the Metro or the infamous #64 Bus in Rome, but if you take reasonable precautions you shouldn't have any problems. I should note that I've ridden the #64 and #40 Buses numerous times, and so far haven't been pickpocketed, despite the fact that I was carrying a very large and expensive Camera (which was in plain view). When I was in Italy several months ago, I noticed an increased police presence in stations and Metro stops, so the authorities seem to be trying to deal with the problem.
"We do not want to have cameras, iPhones ripped from our hands while taking pictures."
It would be a shame to visit two such beautiful cities and not have any photos to remember the occasion. iPhones are probably more attractive to thieves, but you should be fine with small P&S cameras. After all, there will be thousands of other tourists with cameras (and Smartphones), and the majority won't have any "theft problems". Again, I think this has been exaggerated.
"I am elderly and thinking of taking a cane but I really don't need for walking."
If you don't need the cane for walking, what are you planning to use it for?
You may find it helpful to have a look at THIS short video on the the topic. A few things to keep in mind......
- Keep your Passport, credit cards, larger amounts of cash in your money belt. Keep your daily expense money in a more accessible location (front pocket or wherever) and DON'T access your money belt where others can see.
- Practice "situational awareness", especially in more crowded locations. Be aware of who's around you, especially those within arm's length.
- Be especially vigilant if a distraction (a loud argument or whatever) occurs near you.
- Be vigilant when going up escalators or stairs, especially if the person in front of you stops suddenly.
- Don't engage anyone that asks "do you speak English" or wants you to sign a petition.
- You'll probably be approached by sad looking children holding a tin cup (especially in the Metro), perhaps playing a small accordion that produces something resembling music. Your choice whether you want to give them a donation.
- You'll probably see older women, perhaps stooped over with a cane and unsteady on their feet at the entrance to some Churches or other attractions holding a cup. THIS photo shows an example in Rome. They're not hard to spot. Again, your choice on whether you want to make a donation.
- You may be approached by people at ticket Kiosks in larger stations offering to "help" you with the ticket purchase. They can sometimes be persistent, as I found with a group of teenage girls in one of the Metro stops in Milan recently. A polite "NO" didn't work so I simply walked a few feet to the nearest ticket office and purchased a day ticket - problem solved and I didn't have to put up with that annoyance for the rest of the day (the police rousted that group just as I was leaving).
Take reasonable precautions and most likely you'll have a wonderful time in both cities.