You can normally park free at either of El Cortez's parking garages (just flash your players card at the attendant). Weekend nights will be difficult to park....El Cortez's overflow garage will charge to park....and the one adjacent to the casino will be packed. But The Container Park is right across the street.
There are parking meters on the roads surrounding the Container Park. Depending when you go those will have varying levels of occupancy. Less in the day - more so at night.
Most of the other casino parking lots either charge money or require validation inside the casino. Free Valet parking still exists at Downtown Grand - just need to tip the attendants.
pj's tips are probably your best bets. There are also several lots bordering the block of the Container Park. They are smallish and are sometimes manned and ask a fee, sometimes not. Look carefully for signs and instructions at the entrances.