Hancock gets a chance to play hero when he is set free to deal with a violent bank robbery
and hostage situation that has the police stymied. The uniformed Hancock shows up
at the scene of the crime and deftly dispatches the bad guys.

Those scenes were shot in downtown L.A., on Figueroa Street, between 5th & 6th Streets,

That's the west side of City National Plaza, with the actual robbery being staged in the low building
between the Paul Hastings tower (on north) and the CNB tower (on south).

After successfully thwarting the bank robbery, and being hailed as a hero,
Hancock & Ray celebrate over dinner at a fancy restaurant.

That restaurant was real. It was Cafe Pinot, which can be found at 700 W. 5th St, in downtown L.A.

That's right next to the US Bank Tower and the Los Angeles Central Library.

We see Hancock's trailer (again) when Ray's wife shows up there to warn him to stay away.

It's clear that they shot these scene in the hills above Pacific Coast Highway, somewhere
between Malibu & Point Magu, but it's hard to pinpoint the exact spot.

My best guess is a hilltop about half a mile northeast of that whale-throwing beach
(Sycamore Cove), in Point Magu State Park (see the map below). But I could be wrong.

The giant fight scene between Hancock and his super ex-wife (Charlize Theron) takes place at the
corner of Hollywood Blvd & Highland Ave, right in front of the Hollywood & Highland center,
and Grauman's Chinese Theatre.

In the photo above, we're looking east up Hollywood Blvd, towards Highland Ave.

In the photo below, we're looking west/southwest down Hollywood Blvd, towards Orange Ave.

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At the end of their fight, Hancock and his super-ex crash into the building where Ray is delivering
another corporate pitch, exposing the secret that Ray's wife has super powers.

That building is part of the "Century Park" complex, at 2000 Avenue of the Stars, in Century City.
(It's located between the Century Plaza Hotel and the twin Century Plaza Towers.)