My husband and I are traveling to Rome in July for 7 days. We will spend a few nights in Rome and a few nights in a small town called San Giorgio a Liri, where his ancestors are from. I have been to Rome before and done all the touristy things, but this is my husband's first trip to Italy. I have a feeling he won't love Rome (he doesn't like big congested cities), but of course, he will want to see the major touristy things to check them off the proverbial list. My question is: can you recommend a quick way to hit the tourist spots and then ideas for more "off the beaten path" experiences that we can enjoy in and near Rome.

The Gianicolo district is lovely and peaceful.

Second the Giancolo above Trastevere. I would recommend doing a walk through Trastevere up to the Giancolo or reverse. You may see it termed as Janiculum in the American/English guide books. The views are wonderful from up there. Stop and have lunch or of course gelato along the way.

Visit the Protestant Cemetary which is really a beautiful garden--very quiet with Palm trees and other nice trees. The Pyramid is adjacent to it. Walk a few blocks away and have lunch at Perilli--you are not likely to see any tourists there. Hope your DH will enjoy Rome.

There is no quick way to hit tourist spots unless you just take a Ho-Ho bus.( too many IMO).

Quartiere Coppede ( about 15- 20 min by bus from the center) is interesting (small) spot.
Elegant Parioli district( further north) between Villa Ada and Villa Borghese - a totally different side of Rome almost never seen by tourists.

I agree it is good to go up the Giancolo/Janiculum for the great view of Rome. Easier to take a bus or taxi to the top (Piazzale Garibaldi). On the way downhill to Trastevere you can see Bramante's Tempietto

It is hard to know what to suggest to someone who says s/he has done "all the usual touristy things." Rome has hundreds of churches and most people see only a few on any given trip. There are threads on this forum suggesting people's favorites.
If you haven't been to Ostia Antica that is a good half day excursion easy to reach by train