Here is my research. Try Hotel Smeraldo, it may meet your needs.
Preferred location is Pantheon and Piazza Navona
#1 Albergo del Senato (on piazza at Pantheon) 9.3. $984 $1201, $1128, Pantheon patio requires 4 nights and is $445/night.
BOOKED direct-$870e+36e, one double room with breakfast. $970
Hotel Smeraldo 8.9 (between Colosseum and Vatican),affordable $813. 0.4mi from Pantheon , May have street noise
Hotel Ponte SISTO 8.4 $1048
Hotel Navona 8.4 $1077
Albergo Santa Chiara (near Pantheon) 8.7 $1305, $1030
Lancelot (near Colosseum) 8.8 $664
Navona 49 9.0 $1323
Hotel Damaso (near Pantheon) 9.3 $1200
Hotel Artemide 9.3 $1215
Hotel Colosseum 8.4 $819
Hotel Locarno 9.2 $2244
Hotel Nerva Boutique (near Forum) 9.3 $1514
Hotel Hiberia Roma (with view) 8.7 $850
Hotel Pantheon
Marriott Pantheon Iconic 286,000 points
Hotel Abruzzi $1185 annex, $1581 (pantheon view)
The one Boutique Hotel and Spa 8.9 $1591
Boutique Hotel Trevi 7.4 $1056
Hotel Trevi 8.2 $842e with view on their website, good location $892