Here's a map of the HSI surroundings, I'll try my best to explain where's what.
So, the arrow numbered '1' is Sf. Andrei street end / entrance. Arrow numbered '2' is the stairs coming down to Sf. Andrei from Palat street. Arrow numbered 1' is the road that you can get to by going right at the (car) street lights on Splai Bahlui (going from P. Ros to P. Piatra).
By foot, if you come from Str. Palat, go down the stairs and keep going in the same direction until you reach the Sf. Andrei street. Across of you should be a red, modern looking building. Go right and walk about 50 meters - on the left side you have some Christian association and just after that building there's a narrow street (arrow number 4) and a small white plaque saying 'Proprietate privata'. You're on the right path, go left on that street and walk until you'll see a building crossing your path. On the left side there's a gray double door - you're there!
By car, you either come all the way from the other end of Sf. Andrei street (or whichever entry is closer) or, if or some reason you come from P. Ros, via Splai Bahlui, go right at the second light (across Dubet Pyramid) (arrow 1') and go until you reach the Sf. Andrei street. Now, follow the pink marks on the map - go towards the stairs / dead-end and then take the first left, then the first left again, and, of course, left again and you're on Sf. Andrei street, going the correct way. 20-30 meters after you got back on Sf. Andrei, make a right to HSI.