The first thing you should do after entering the Hall of Heroes is to proceed to the left corridor (the one with the motorized patriot) and search the ticket office. There's a Voxophone #30 on the table on the other side of the door and you'll also find one lockpick under the usher's desk.
Leave the ticket office and you'll soon encounter Slate's men. Fight your way to the big hall with Comstock's Statue and after talking to Slate deal with his people. Once the battle has ended go to the same room the enemies came from.
This room contains several useful items, including a new lockpick found under the shoe of a statue located in one of the corners.
Check the table found opposite the statue in order to collect one more lockpick, as well as a silver tab and Infusion #8. Once you're done exploring this room proceed further into the Hall of Heroes.