Regarding your hotel location, it's in the Prati district. While removed from the larger tourist attractions, it's also less touristed. We were just one block off of Viale Giulio Cesare and enjoyed that area very much. I will note that we are also hearty walkers - were in our 50's on that trip - and hoofed it everywhere; from our accommodation down to the Colosseum, to the Vatican, through Villa Borghese, etc. Rome is such an interesting city to experience from the sidewalks and backstreets!
There are two metro stops for Line A along Viale Giulio Cesare: Lepanto and Ottaviano: Ottaviano is scheduled to close at some point this spring for work related to the 2025 Jubilee. Spagna, near the Spanish Steps, will also close and the metro trains won't stop at either of them during the renovation work. Lepanto, also on Line A along V. Giulio Cesare, will be unaffected as will Cipro, nearer the Vatican. As closure dates haven't been posted yet, it's possible that won't happen until May. Even if it does - and the metro lines don't service the heart of the historic center anyway - there are always your two feet or buses. :O)
You will only have 5 full days in Rome - arrival day is a partial that doesn't usually count due to potential jet lag - so I'd go easy on the day trips. No, do not rent a car: take the trains.
Yes, get a guidebook and read up on the what Rome (and Florence) have to offer and what appeals. Understand that the Italian State Museums are generally closed on Mondays, and private museums can have a weekly closure day as well. Your trip is also occurring during high season, and the most-desired/least expensive tickets, if available at this point, are quickly disappearing. For end of April, I'll highly recommend booking tickets or tours for the most-visited attractions as soon as you can; don't dawdle!
ALL advance, timed-entry tickets or tours are "Skip the Line". That does not mean they skip the security-check lines. No one can skip those.
What to see in Florence? Depends on your interests but its biggest claim to fame is as the "Cradle of the Italian Renaissance" so it's very heavy on art and architecture. With limited time I'd skip the Uffizi and Palazzo Pitti unless you're REALLY into art. Both were must-sees for me but I had considerably more time to work with than you will.