One week in Italy (Rome) advice on a 2nd destination or side trips?

I'll be taking a side trip to Naples and Pompeii while I'm in Rome. That would be interesting if you like history.

I suggest staying in Rome and making one or two day trips out. Not having to change hotels will save you a lot of hassle and money, and Rome itself can easily keep you busy for 4-5 days.

If you're interested in Pompeii but don't want to go that far, check out Ostia Antica. It's about 45 minutes from Rome and is a pretty intact old Roman town. I really enjoyed it. It used to be the old seaport, but the river dried up and moved away. The nearby modern town of Ostia Lido is on the water, however.

If you're interested in smaller, pretty towns, check out Orvieto which is an hour train ride north of Rome and has a fantastic Duomo as well as several other interesting sights.

Florence is doable as a daytrip from Rome, but it's a pretty long one so I'd recommend not squashing it in there this time. Venice is not convenient enough to fit in with only a week.

There is plenty to do in Rome even if you stay there for a month, but you'll probably want a change of pace. Ostia Antica & Ostia Lido are a good economical daytrip, especially for late August.

I think your brother will enjoy Sorrento, Pompeii & maybe Capri. From your entire stay take away two days and one night. Start early in the morning from a train and arrive @ Naples and take another train to Pompeii, by 1pmish you should be there. Explore the area and catch 30 minute train to Sorrento. Saty overnight and try and find a cheap place, I recommend that you donot leave your hotel in Rome, get additional one night at Sorrento so you donot have to travel with luggage.

Evening explore Sorrento...next morning, take a boat to Capri...explore till afternoon, come back to sorrento and take the train back to Naples and from Naples 1 hrs ride to Rome...I think , your brother will enjoy it. I know it is a lot but give it a shot.

You can do the same with Florence , 2 hrs train ride from Rome, stay overnight...come back the next day.

Have fun..and soak in the experience

There's plenty to see in Rome for a week. If you do a sidetrip, definitely Naples (for Pompeii, Herculanum or Sorrento) rather than Florence, which is more museums and there are already plenty of those in Rome. Venice is too far. If you want beaches, stay in Sorrento for 2 nights and bus out to the Amalfi coast from there.

Since economical is one of your criteria and this is your first trip to Italy, I would suggest basing yourself in Rome and doing side trips. Both Ostia Antica and Ostia Lido (Rome's beach) can be reached in 45 minutes using a 1 euro transit ticket (2 euro R/T) or a transit pass (for example, 4 euro for unlimited travel until midnight). The beach will be busy in late August. Orvieto is an inexpensive 1 hour side trip because the train is a regional (the least expensive). The same train continues on to Florence, taking about twice the time as the fastest direct train but at about half the price. If you decide to visit Pompeii (long side trip), take the IC (inter city) train to Naples. It too is about half the price of the fast trains, but only takes about 20 minutes longer.