For restaurants, I suggest Due Colonne at Via dei Serpenti 91 (near Piazza del Quirinale); and Gino e Pietro at Via del Governo Vecchio 106 (near Piazza Navona).
The only suggestions I would make about your itinerary would be to get to the Colosseum, the Pantheon and St. Peters earlier in the day. Colosseum and Pantheon both open at 8:30 am -- be there when the doors open! It will make your visits much more pleasant, as you'll have the sites nearly to yourself. Head for the Pantheon even a little earlier, and stop for a coffee and pastry at Tazza d'Oro, a block or so northeast of the Pantheon. St. Peters opens at 7:00 am. We got there about 8:15 on our visit last May, and that was too late. The security line was already 30 minutes long, halfway around the Piazza.
Also, be aware that the Basilica of San Clemente is closed from 12:30 pm until 3 pm daily.
My grandson and I spent five days and four nights in Rome last May. We stayed at a convent near Piazza Venezia. The itinerary went like this (all by walking, unless noted):
Day 1: Arrive at FCO, FM1 train to Ostiense station. Walk past Pyramid of Cestius and WW2 battle monument at Porta San Paolo, Baths of Caracalla, Circus Maximus and Colosseum to the convent. After checking in and resting up, we walked a circle route via the Colosseum, Arch of Constantine, Circus Maximus, Bocca della Verità, Forum Boarium, Theater of Marcellus, Campidoglio, and view of the Imperial Forum (in the rain).
Day 2: Walk to Colosseum at 8:30; then Palatine Hill, Imperial Forum, Ludus Magnus, San Clemente, St. John Lateran, St. Peter in Chains.
Day 3: Walk past Quirinal Palace, Trevi Fountain, stop at Tazza d'Oro and arrive at Pantheon for 8:30 opening. Then Santa Maria supra Minerva, Largo Argentina, Campo dei Fiori, Piazza Navona, Hadrian's Bridge, Ara Pacis, Piazza del Popolo, Spanish Steps, Via Veneto, Piazza Barberini, Via Rasella. Return to Colosseum and Campidoglio for late afternoon/sunset views.
Day 4: Metro to St. Peters, then Metro and Lido trains to Ostia Antica.
Day 5: Metro to Tiburtina rail station for departure.
Photos here.