An unusual number of the best things here are free — the observatory, the Getty and The Broad all charge nothing to get in — so the real cost of a day in Los Angeles is parking and time in the car.
Griffith Observatory
Owned and run by the City of Los Angeles Department of Recreation and Parks, and free to enter. Open noon to 10pm Tuesday to Friday, 10am to 10pm at weekends, closed Mondays. There is paid parking immediately below the building and free parking further downhill, which is the cheaper option if you do not mind the walk up.
The Getty Center
1200 Getty Center Drive, free to enter but requiring a timed-entry reservation. Open 10am to 6:30pm Tuesday to Friday and Sunday, until 9pm on Saturday, closed Monday. Parking is the actual cost: $25 per car, $15 after 3pm, $10 after 6pm, and free on Saturdays after 6pm.
The Broad
Contemporary art museum at 221 S. Grand Avenue downtown, with free general admission. Open 11am to 5pm Tuesday to Friday, until 8pm on Thursday, 10am to 6pm at weekends, closed Monday. Kusama's Infinity Mirrored Room is also free but wants an advance reservation; extra slots for the next day are released each evening.
LACMA
The county art museum at 5905 Wilshire Blvd on Museum Row, and the one major museum on this list that charges. Open 11am to 6pm Monday, Tuesday and Thursday, 11am to 8pm Friday, 10am to 7pm at weekends, and closed all day Wednesday — the closure catches people out more than anything else here.
Grand Central Market
Food hall at 317 South Broadway that has been operating since 1917, open 8am to 9pm every day, though individual stalls keep their own hours. Tacos, ramen, fried chicken and coffee at counter prices in the middle of downtown; go at an odd hour if you want a seat.