Housing near or in arts district

I'll be in Los Angeles for the month of October (from Oct 4 - 31) and I'm looking for affordable housing. I don't mind sharing with one or two people. My budget is 1000-1200 including utilities. I need it to be accessible (minimal stairs or none if possible) and close to good supermarkets and public transportation (especially bus stops), ideally also close to a swimming pool and gyms. Please message with any leads, or please share recommendations for good websites for local short term housing. Thanks