I have been to LA and Hollywood for 2-3 days and I along with three other friends stayed in Hollywood very near to Hollywoods famous walk of fame. The city itself is huge and well spread-out, you may be travelling for 2 hours but still not out of the city. The places we visited were Universal Studio, Santa Monica/Venice beach and downtown financial district .
One day was spent in Universal Studio and it costs $50 for a single day but let me tell you that its worth it. They are so many items and shows which you could never experience anywhere.
The best time to visit Santa Monica/Venice beach is on a weekend when beach is teeming with people but no crowding. The venice beach is just adjacent to Santa Monica just given a different name. There is a flea(?) market also at Venice beach where people sell weird items.
Downtown is the place to see skyscrapers one after the other and general roam around and that is what we did.
The best part of the city we liked is fare for public transport: metro trains and buses are integrated and a day pass is just $3 (around Rs. 135) which is very cheap and service is efficient.