I think you have this back to front. An authorised taxi from Taxi Green at the airport will cost S/.45, if you try your luck with a taxi pirate out the front of the airport then you are far more likely to be charged "dollars for soles" i.e. US$40-45.

Well worth joining the short queue inside the terminal to get a guaranteed service, safety and a mandated price.

For photography purposes in Lima you might want to consider Barranco which has a bit of character and hostels with private rooms well within your budget.

Santiago: Plenty of cheap places to stay in Bellavista and close to a lot of streetlife, Parque Forestal, the Bella Artes district and walkable to the centre. Stayed there last week and took my own DSLR out, all together felt safe but towards the end of the day on the back side of Plaza de las Armas began to feel a bit like Bogotá. Our digs for one night cost $40 and had thumpingly quick 9 Mbps internet.

As Siempre Viajando says the bus transfers are reliable and cheap. For Bellavista we got the Tur Bus transfer to Terminal Alameda which is adjacent to Metro Universidad to Santiago which in turn is 4 or 5 stops to Metro Baquedano.

One thing I noticed a week ago today is that some metro stations share entrances with small shopping centres which are closed on Sundays. The metro IS open but sometimes you have to walk around a bit to find the dedicated entrance.