Downtown is a traffic mess. If you don't need to take a car for logistical purposes, take public transit.
Most long bus lines that run toward downtown will stop in the Pershing Square area. From there, it's around 6 blocks up to City Hall.
If you can't walk it, you can take the Red Line train from Pershing Square to Civic Center station, which is 2 blocks from City Hall. A bus also runs along 1st St if you can't walk the 2 blocks.
Bus fare is .25 per boarding. A "Day Pass" is , and covers you for boarding all day long.
If you are coming from distant points, you can park near the endpoints of the Red Line in North Hollywood, and the Gold Line in East LA/Montebello, and the Gold Line's northeastern branch, and at some point along the Blue Line, and then ride the train from there.
Most areas in LA are metered, unless you park a ways away. (There are some spots on 4th st that aren't metered.)
Afterward, the eating opportunities nearby are numerous. Little Tokyo, Chinatown, Olvera St., the gentrified old Downtown as well as the ungentrified parts, and even the mall underneath City Hall. The garment district and food districts are also happening on the weekends, in a big way.
It's good times if you're not a Nazi.