Continue down Sunset to La Brea. Turn left on La Brea until you get to Wilshire (about 2 miles) Turn right on Wilshire. As you pass Curson, look for metered parking on the right in front of Hancock Park near the Page Museum and the La Brea Tar Pits. If there is no parking available on Wilshire, turn right on Fairfax and right on 6th Street to park on the other side of the park or park in one of the pay lots. There are entrance gates from 6th Street and from Wilshire, but the biggest tar pits are near the Wilshire entrance.
Take a quick stroll through the park to see these active tar pits where more pre-historic fossils have been discovered than anyplace else on earth. Active excavations are under way and there are daily tours of the current excavation pit at 1 p.m. Fossils from these pits have found their way into museums all over the world, but the largest collection is here at the Page Museum.
If you're ready for lunch head up Fairfax to 3rd Street to the Farmer's Market to grab a bite at one of the many food vendors in this permanent market building. If you finish lunch quickly, you might have time to stroll next door for some shopping or celebrity spotting at The Grove.