Here's what you'd want to do. Read blogging.la's post on the subject & the attached comments.

"• A morning stroll through Chinatown segues to breakfast at Philippe's (Alameda Ave, north of Sunset/Cesar Chavez) followed by a walk through Olvera Street before heading over to explore Union Station and hopping the Red Line ($3 per person for an all-day pass)
• Exit the Civic Center station (first stop) for a short walk to visit to check out the Disney Concert Hall and maybe MOCA across the street then head south on Grand to 5th for a looksee at the Central Library and then the Biltmore on your way to Broadway to marvel at the historic Bradbury Building (304 S. Broadway).
• Head south on Broadway to 7th Street passing the facades of several of the district's grand old theater palaces and even more bootleg DVD/three-card/shell game vendors. If you need a bite there's camp/kitchy Clifton's Cafeteria on Broadway north of 7th, then head west a couple blocks to the 7th Street Red Line station and go underground to get back on a train marked either Wilshire/Vermont or North Hollywood.
• Get off at the next stop (Westlake station) and do a walkabout around the revitalized MacArthur Park (maybe take a couple paddle boats out on the water?). When you reboard the Red Line at the Westlake station make sure your train is labeled "North Hollywood."
• Exit at the Hollywood/Vine station and you'll soon be across the street from the Pantages Theater where you can then head west along Hollywood Boulevard's "Walk of Fame" all the way to Mann's Chinese Theater with various touristy points of interest in between. Perhaps lunch at Musso & Frank's.
• From the Chinese Theater you're only a couple blocks away from Mashti Malone's Ice Cream shop on La Brea, which has excellent exotic flavors such as rosewater (and their butter pecan is the bomb).
• If your beat, you can head back up to Hollywood and Highland to catch the downtown Red Line train that'll take you all the way to Union Station
• Or if you've still got some energy left, a walk from Mashti's south on La Brea to Sunset Boulevard then east, while not loaded with sights, will eventually bring you past Amoeba Records and the Cinerama Dome / Arclight Theaters. From there if a movie's not in order, then head north up Vine Street to Hollywood Boulevard to get back to the Hollywood/Vine Red Line station for the downtown-bound train that ends at Union Station."

Almost makes me wish I lived there. ;-) I have often wished that I had a greater appetite for metropolitan cities, and also wondered what life would be like if I had found myself living the 'Notting Hill" life in London after college. This post is an example of why. There's a lot to celebrate in a city, if you know where to look and all....