The apartment is LOVELY, very cute and also in a very safe area. Obviously the usual rules apply in any big city - be savvy, don't walk around with headphones, etc, but I never felt unsafe walking the streets at 1am after a late dinner.
The apartment is maybe 7 mins away from the Miradouro da Graça, which in my opinion has one of the best views of the city; it's also about 20 minutes hike away from the Castle of Sao Jorge. (The castle looks far, but it's really not that bad!) It's also pretty centrally located - about 6-7 mins away from the Martim Moniz metro, which gets you easily to anywhere in the central city. That being said, I spent most of my time walking instead of taking the metro, so perhaps you won't need that that much...
Overall, I LOVED my stay here. Nuno's team was very organised, patient, and they were excellent in recommending places to go and eat. Definitely worth the stay here. Cannot recommend it enough.