Wife and I loved these places. Plus they were convenient for seeing sights.
Bir & Fud
Via Benedetta, 23, 00153 Roma RM, Italy
+39 06 589 4016
https://goo.gl/maps/TRCtzJzKyjm
This place is across the alley from Bit and Fud and had Cantillon.
Ma Che Siete Venuti A Fà
25, Via Benedetta, 25, 00153 Roma RM, Italy
+39 06 6456 2046
https://goo.gl/maps/LRTaHm3Myxu
Johnny's Off License Campo de' Fiori
Via dei Balestrari, 9, 00186 Roma RM, Italy
+39 06 3107 4795
https://goo.gl/maps/csSxn1oEd8u
Great bottle shop, cool owner. Again, very convenient.
Not a beer place, but my favorite restaurant in Rome. Hard to get in, but worth it. Again, very convenient if you go to the Pantheon (my favorite place in Rome).
Armando al Pantheon
Salita dei Crescenzi, 31, 00186 Roma RM, Italy
+39 06 6880 3034
https://goo.gl/maps/Was8yxFSBCB2
Edit: should have refreshed my phone before posting all this.