Santiago is long and the metro is good, so the real question is which stretch of Line 1 you want to wake up on: the museum-and-restaurant core, comfortable Providencia, or the quieter east.
Lastarria and Bellas Artes — the walkable core
Between Cerro Santa Lucía and the river, with museums, bookshops and restaurants at street level and metro stations on either side. Central and priced accordingly, and noisy on Friday and Saturday nights.
Providencia — the sensible middle
The Line 1 stretch from Manuel Montt to Los Leones: residential streets, supermarkets, mid-range hotels and apartments, and about ten minutes on the metro into the centre. The best ratio of value to hassle in the city.
Barrio Italia and Ñuñoa — quieter and cheaper
Low-rise streets of old houses, design shops and cafes east of the centre, with Ñuñoa's plaza just beyond. You trade a less direct metro connection for calmer nights and lower rates.
Practical: stay within reach of Line 1
Nearly everything a visitor does is on Line 1 or one transfer from it, and a bed within a ten-minute walk of a station removes most of the city's distance problem. Santiago Centro west of the Plaza de Armas is cheap but empties after office hours, which is worth knowing before booking on price alone.