West Hollywood is a must when visiting  LA  -- it is packed with places worth visiting.

Visit Bodhi Tree bookstore on Melrose, close to the crossing with San Vicente. also stop by for a cup of tea at elixirs  peaceful  garden , right across the street from the Bodhi Tree.

At  night you can hit the Sunset Strip. The Standard Hotel is a favorite, cool,  very LA, and there is no cover for the lounge or to have a drink by the pool , which has a fantastic view of the city below.

Santa Monica Boulevard gets really  busy  at night, most of the gay bars are here, although most of LA is gay friendly as well. Here on robertson is worth a drink.  

Silver Lake's  Akbar is a great bar in a very different and unique neighborhood,  just to experience another side of LA culture