I would thoroughly recommend Brendan and Stina's apartment as an affordable to place to stay whilst you explore L.A. The location is brilliant as it is only a few minutes walk from the Metro Station and the buses on Sunset which take you to a number of key sights! They are also within walking distance of Hollywood, Los Feliz and Silver Lake.
Brendan and Stina were both wonderful hosts who made me feel very welcome as a solo traveller. Their having two pet dogs was an added bonus for me!