Downtown L.A. used to be a dirt hole, and for sure in some corners it still is. But downtown also has an up- and coming hipster scene. The art district with its galleries (like the Swiss “Hauser & Wirth”), lots of hipster coffee shops and overpriced hipster boutiques. That all basically two blocks away from one of the largest homeless spots. Besides, downtown L.A. with its modernized loft apartments is (one of the) the place(s) to move to (if you want be in the city and not near the beach in Venice or Santa Monica).
Downtown offers, besides the art district: MOCA (modern art museum, but to be honest the exhibition was not worth the 15$ admission), The Broad (free! and beautiful architecture – but register in advance otherwise there will be a 30-50 min waiting line), the fashion district (feels very much like Southern American markets) and the Grand Central market with all its food stalls (Mexican, great bread, Chinese, etc.).
Downtown nightlife with its rooftop bars and restaurants – and a soon to be open SOHO house – is worth a visit as well.