There are some reliably constant sources of Uzi's in the game (note -- unless you are doing Case 1.1, thses Uzis do not appear if you have one in stock already):

(1) The fountain in Al Fresca Plaza. Note, having an Uzi in stock will prevent this item from spawning when the Al Fresca map is loaded. It's best to complete the Case files until this area of the map is opened easily (assist Brad, fight Carlito #1 on day one).

(2) In Paradise Plaza, head up the stairs to level two (the stairs next to P113 Kids Choice Clothing). On the landing mid-way up the stairs, jump and mantle onto the blue store marquee. Follow the wall until you are over P116 (Shoe Kings). The Uzi's placement should be obvious.

(3) In the Food Court, locate F103 (Chris' Fine Foods). There is a signboard that has a cook's cariticature. Mantle onto the dining booth sidings, then mantle again onto the cariticature signboard. The Uzi should be on the top.

(4) The maintenance tunnel warehouse. This is the same room as the maintenance tunnel key. On the map, this room is underneath Leisure Park, and may be considered "just south east" of stall W107.

(5) In Wonderland Plaza in the play area by the maintenance tunnel entrance, you need to zombie ride to the toy playhouse. The uzi is on the house's roof.

(6) In the leisure park, goto the entrance of the parking lot, turn right & go to the corner there should be a tree with a rock under it, the Uzi is up in the tree.

(7) In Entrance Plaza, go near the escalators. You will need to use the Zombie Ride to reach it.

Submitted by MasterChief89 (ungguy89), kinwulf, hod85