The Culture Alternative  
This section I’d like to start off with a place that will take a considerable amount of time to explore and you’ll never know that it’s raining outside: The Catacombs scattered all over Rome are just this. The Catacombs are basically ancient burial grounds mostly noted for Christian ditto, however a considerable amount of Jewish and Pagan burial grounds have been found alongside the Christian one, either mixed or separately. The Catacombs are interesting in a lot of different ways and I’m sure your exploring will take its time.

Secondly there is the Sistine Chapel which is completely protected from any rain. However, be there early in the morning to secure a speedy entrance as queues can get incredibly long. If you’re first in line you don’t get wet, and you spend a few hours inside depending on your level of interest. Definitely, the Sistine Chapel is a good alternative to spend a rainy day on.

If you’re interested in Roman history and the sculptors and artists that have been Rome based over the centuries, then I strongly recommend you to visit The Borghese Museum and Gallery on Piazza Scipione Borghese, 5. This wonderful museum hosts works of famous influential artists and sculptors including G.L. Bernini, Canova, Correggio and Raphael.  The museum will take quite some time to explore thoroughly and in addition to this, there is a nice bookshop and café facilities available. All of which are completely rain-free.

Let’s continue on the art-track and move onto contemporary art. If you prefer modern art there is a truly amazing gallery centrally located that you shouldn’t miss: National Gallery of Modern and Contemporay Art on Viale delle Belle Arti 131, just a few blocks north of Piazza del Popolo. This gallery has a huge selection of works by world-famous artists including Macchiaioli, Manzù, Matisse, Picasso and Modigliani. There is also a coffee shop and a bookstore/gift shop for the one who’s interested.

Lastly we have the Vatican Museums on Viale Vaticano. These museums are interconnected in a large and complex network of museums and it will take you forever to see everything. Nonetheless it’s a nice way to spend a rainy day and surely it will give you new knowledge and insights about the Vatican and the art scene surrounding it throughout the centuries.

The Landmark Alternative
As most monuments are in an open space area there will not be too many of those on this list. However, there are some nice buildings with a rich history that allows you to spend a few hours just exploring and experiencing history without having any rain fall on you.

The first one is perhaps the most obvious one: Basilica di San Pietro or St. Peter’s Church. Once you enter this truly astonishing construction of artistic and architectural brilliance you can feel the centuries of history and religious and political importance hit you as if you walked into a wall. Beautiful being an understatement, this church has a great and mysterious atmosphere to it. Also once you get here, I recommend you take the stairs up to the top of the cupola. Not only will you see the interior from an elevated perspective, but you also get a nice view of Rome and the Seven Hills.
The second building isn’t going to take too much time to explore but is nonetheless worth a visit. The Pantheon comes from old Greek and the approximate meaning of which is “to every god”. The meaning of pantheon is actually quite accurate as the Pantheon has belonged to different faiths and served many different purposes throughout the centuries. As mentioned above, The Pantheon isn’t going to take a lot of time exploring, but it shelters you from the rain and it’s really a place you have to see when you’re in Rome.

My final recommendation is sort of a combination of a museum, a playground and a teaching facility in a fun and interactive environment. Yes, this place is for families with children. It is called the Explora Children’s Museum. It’s a place specifically designed for children and it features miniature stores, “driveable” vehicles etc. The kids love it and it’s a great place for the parents to sit down and rest for a moment while the kids go wild. This kind of children adapted “playground-museum” is a rare occurrence in Italy and if you’re in Rome during a rainy day and can spare some time for the kids – why not go here?

The Shopping Alternative
The first large indoor department store I come to think of is La Rinascente (meaning “rebirth” in Italian). In fact, I think La Rinascente is the largest Italian department store country-wide. Paying a visit to this well stocked wide-varied plethora of stores gathered into one will certainly give you a wonderful shopping opportunity while providing a decent way of spending a few hours indoor on a rainy day in Rome. Keep in mind though as a nation-wide quite upscale department store, the prices tend to be a little bit heft. La Rinascente can be found on Piazza Colonna and Piazza Fiume.
Secondly, albeit smaller scale but nevertheless useful and trendy is Coin on Cinecittà shopping mall, Piazza di Cinecittà, Viale Palmiro Togliatti, Via Mantova 1/b, near Piazza Fiume and Piazzale Appio. There are plenty of items to be found in Coin at cheaper prices than La Rinascente, especially if you have children. Furthermore, Coin has an excellent section for household items.

The afore mentioned activities are just a few recommendations of what I could imagine myself doing during a rainy day in Rome. After all, Rome and the sights and attractions herein are sort of dependent on nice weather due to distance and the very nature of the outside environment, so maybe this list could give you an idea of measures to take lest the worst happens – a rainy day in Rome.