Spent a week long holiday at Rodrigo's in the heart of Barrio Alto. Very helpful before arriving, giving useful directions and accommodating an early arrival. The apartment itself was clean, well furnished with an authentic feel and great views from the balcony (a couple outside seats make it perfect for breakfast). Despite Barrio's noisy reputation, the apartment is on a quiet street and high enough (you'll get used to the stairs) that we weren't woken up even on weekends.
It's conveniently located close to where the free tours leave/a minimart for food, about 10 minutes walk to Cais do Sodré station for the beach/Belem.
Overall, I would thoroughly recommend the host and apartment for a couple looking to enjoy an authentic stay in Lisbon.