This is one of those non-responsive posts that this board is so famous for...
I often have a 3 a.m. drink with the nightman from H. Cantabrico across the street at the Bar Nueva Galicia. Great location, looks good from the outside. I have considered staying there but the view from the website doesn't look as good (for the money) as the Adriano.
The Gran Via is ok until 2 a.m. or so. Head south of Sol where all the clubs are for more people and more safety. North of Gran Via can be dicey around the Telefonica building late at night.