Truly impressed by some of the contributions here. I visit Italy once or twice a year. It’s my second home. The OP is in the unfortunate position of only having seven days to see Italy. With this limited time I can only suggest it would be best to pick a city or a region to concentrate on. That way you'll be able to immerse yourself better in the local culture. Italy is so diverse, so it is important to pick one or two themes: food & wine, art, antiquities, nature, religion, etc. Trying to do too much will become stressful.
If your intentions are to stay in Rome, the seven days will still not be enough. However visiting the major attractions like the Vatican (St Peter's basilica and Museums), Trevi Fountain, Piazza Navona, Pantheon, Colosseum, Palatine Hill, Roman Forum, Ostia Antica and Via Appia Antica can take three or four days. Then you could immerse yourselves into the local culture (Trastevere, Testaccio, Jewish Quarter, etc.). My suggestion is if you really do want to see a bit of Italy outside of Rome you could visit Florence and the Amalfi Coast by catching the Frecciarossa/Frecciargento fast trains from Termini station. These could be day trips. If you decide to do this make sure you book in advance if you want cheaper rates, up to 120 days ahead. You can still book a day or so beforehand if not sure. Your seats will be allocated but be sure not to miss the train(s). If you do you will have to change the bookings and lose precious time. Train bookings can be done directly on the Trenitalia website. If you have a car at your disposal and are comfortable driving, then by all means go into the countryside. Head north into Tuscany and Umbria, or even Abruzzo to the east. Even if you don't make plans to visit a particular town or city you will always find something to see and do and places where to eat (even cheaply).
A few of bits of advice. If you happen to be in Rome on the first Sunday of the month you’ll find national museums will be free. There are also civic museums but these will only be free to the locals. The Vatican Museum is separate and not part of this scheme. If any of your party is disabled, do take your disability card. The one used for parking will do. The disabled person and his/her carer will be given free entry and preferential treatment. This is especially good at St Peter’s basilica (the Vatican) where there can be very long lines in the hot sun.
As for thieves, unfortunately yes. There are plenty of thieves in Rome. They are not Italian but mostly gypsies (Roms) and these will congregate at the Termini station and at bus stops or crowded places. One notorious place is the terminus of bus 64 in Piazza dei Cinquecento, the square at the front of the Termini station. This is where many tourists catch the bus to the Vatican. You need to watch out for squads of young gypsy girls. They wait until the chaos of boarding to pickpocket. Do make sure no wallets or handbags are in sight. Inside the Termini station they will approach you with the excuse of trying to help you. Tell them to go away and it doesn’t matter in what language!
If you had more time some of the suggestions in this thread would be great too. I have my own suggestions but I wouldn’t have space.
Cheers
