Hi and welcome to the forum, Marla! You must be so excited about this trip! :O)
Question? Are you staying 7 full days (8 nights) in Rome or 7 nights (6 full days)? It's just good to have an idea of how much time you really have to work with. As well. Lake Como is not a day trip from Rome, and even if planning to stay overnight will eat a big chunk of a day just to get there. You'd also want to plan to fly "open jaw", meaning into Rome and out of (likely) Milan Malpensa or vice versa to avoid backtracking.
Yes, Italian trains are great. Other than maybe the Leonardo Express into Rome from Fiumicino, whether you'll need to use them or not depends on whether you end up splitting your trip OR taking a day trip to a less time-consuming location.
Hotels with a view.... if finding one with some sort of view from your room (and that you can afford) is problematic, don't overlook those with rooftop terraces you can use during down time. Some of them provide bars or you can BYO (we have.)
Rome has simply oodles of things to see but one person's must-see can be another's not-so-much. Some of us can provide lists of must-do churches (for us) as long as our arms but that might not be your thing. Galleria Borghese? A must on my list! A walk on the Appia Antica? Another personal favorite. As you'll be there in May, the municipal rose garden (Roseto Comunale) on the Aventine will be in bloom, and you can combine that with a visit to very old Santa Sabina, a captivating view of Rome from the orange garden (Giardino degli Aranci) next door to that basilica, and a peer through the keyhole on the gate of Knights of Malta. There's a nice view of the Palatine from the rose garden as well.
https://www.turismoroma.it/en/places/basilica-saint-sabina-allaventino
https://www.turismoroma.it/en/places/savello-park-or-orange-garden. (Nice place to enjoy a packed-along snack)
https://www.turismoroma.it/en/places/villa-magistrale-sovereign-order-malta-aventine. (keyhole)
https://www.turismoroma.it/en/places/rose-garden. (notice the menorah shape of the upper garden)
Up for a longer walk from the keyhole? Continue over the top of the hill and down to the Protestant Cemetery (Cimitero Acattolico - near Piramide metro station) to visit the resting places of John Keats, Percy Shelley, sons of Percy and Mary Shelley, Johanne Goethe and Axel Munthe, beat poet Greg Corso and other notables. William Story's original "Angel of Grief" is here as well. As Shelley himself wrote about this green and quiet space:
"John Keats died at Rome of a consumption, in his twenty-fourth year, on the — of — 1821; and was buried in the romantic and lonely cemetery of the protestants in that city, under the pyramid which is the tomb of Cestius, and the massy walls and towers, now mouldering and desolate, which formed the circuit of ancient Rome. The cemetery is an open space among the ruins covered in winter with violets and daisies. It might make one in love with death, to think that one should be buried in so sweet a place.” Percy Bysshe Shelley, preface of “Adonais”
https://cemeteryrome.it/about/about.html
The Pyramid of Caius Cestius is also right there as well as the 3rd-century Aurelian city gate of Porta San Paolo. Assuming your feet might be shot at this point (ha!) take the metro back to Termini or another station nearer your hotel. Or a bus. Or tram.
https://www.turismoroma.it/en/places/porta-san-paolo
(Edited a typo)
