Hollyhock/Barnsdale is still closed. Still, many examples of Frank Lloyd Wright architecture abound around town if that's your interest. Check out
www.laconservancy.org for information about historical preservation in Los Angeles. Despite our relative youth, at least as compared to East Coast and international venues, Los Angeles is teeming with fascinating examples of architecture, from '50s Googie buildings to Bachelder tile to Art Deco. If you're downtown on a Saturday morning, the conservancy runs walking tours starting from the Olive Steet lobby of the Biltmore Hotel at 10 a.m. on Saturdays. A great view of the city most locals don't even experience. make rezzos on their website. Of particular reknown is the Broadway Theater district tour, showcasing the movie palaces of the 1920s, that are now largely used for retail stores. Some fascinating stuff on that tour.
Walking around certain parts of Los Angeles' downtown is extremely safe. I would stick west of Main Street and north of Third. Not so coincidentally, that's where most of the sites you'd want to see are located. Check out the Bradbury Building, made famous in Bladerunner and countless commercials on Third and Broadway, and as long as you're there, check out the LA Central Market across the street, which features a melange of LA's ethnic comunities selling foodstuffs and produce of all kinds. Then walk up the Angel's Flight Steps (a funicular used to run there but was stopped in 2002 after a man died on it) up to California Plaza which has dancing water gardens. From there, you can go north to the Music Center, and even further north to the new LA Cathedral.
For a wonderful ethnic experience, go even further north to the Empress Pavilion on North Broadway on a weekend morning for dim sum. It's Los Angeles' largest restaurant (seats 900) and every seat is filled and women walk by pushing trolley carts filled with the most delectable little morsels. You can eat really well for under $10.
Another great ethnic dining experience is shabu shabu. My favorite restaurant for that is the aptly named Shabu Shabu House on Second Street just east of Los Angeles in Little Tokyo. Usually a wait, but well worth it. Look at the locals eating before you sit down for tips on how to swirl your thinly sliced beef in the boiling vat of seasoned water in front of you.
More if it comes to me.