You can do the Art Collector sidequest all at once, or you can gather the paintings gradually as you naturally progress through Silent Hill's neighborhoods. We will start by showing you the map of the locations of all the paintings, the art gallery, and the final treasure, and then proceed to a more detailed walkthrough of the quest. For those just interested in the solution to the Crypt Gate puzzle, you can scroll down to the end of this walkthrough.

There are nine paintings total. Three of them are already at the art gallery. The locations of the other six are as follows:

Silent Hill Downpour Painting Locations Map

Silent Hill Downpour all paintings locations

1: "Despair".  Hillside - Inside Police station, in small barricaded room near dispatcher radio.
2: "Sunrise". Hillside - In underground entrance.
3: "Certainty". Pearl Creek - In Storage Unit, in alley north of Pearl Creek Underground Entrance. Keypad code is "827" (from mystery object)
4: "Wonder". Pearl Creek - In ground floor of the apartment used to enter Pearl Creek from Hillside
5: "Hope".  Chastain Heights - From St Maria's Monastery go east to find a hardware store. Get storage key from cash register and unlock room nearby, painting is in crate.
6: "Freedom". Pleasant River. Go west on Rice st. and open the door to the back of the van.
7: Art Gallery. Pearl Creek, south of Centennial Bldg.
8: Burial Chamber. Monroe Cemetery.

In Pearl Creek, South of the Centennial building, locate the entrance to the Art Gallery. The art gallery is roughly in the NE of the block bordered by Brite St in the North, Lansdale Ave in the East, and MaCammon Street to the south. Enter the gallery.

Go straight in the corridor and enter the second room to the left. You find the following two mystery items in this room:

Finders Find Art & Appraisals
October 3rd
Dear Mr Rice,
The Delalle painting in your collection needs to be in a public gallery, not the private home of an eccentric recluse who selfishly hordes such treasures for his sole enjoyment. I have tried repeatedly to get you to accept my generous offers to purchase the painting, but once again you rebuff me, leaving no choice but to take dramatic measures.
It would be extremely unfortunate if certain details regarding your son's suicide were made public. Give me the painting, and I'll assure you that these allegations will never see the light of day. Refuse me, and face the consequences.
Sincerely,
Melissa Matlan

How large is the map? 3x3 grid? Maybe I don't need the entire map to find the treasure. Who has the missing paintings? (Cross-check with Art Collecto Quarterly. Who's bringing New England 19th century arts?)
Mr Rice (Won't return cals)
Mr Brite (crossed out)
Mr Barker (Refuses to sell)
Mr Steel (crossed out)
What do the symbols mean???
Native American. Maybe Algonquian? Call Pat at SH History Society, maybe he knows?
Ravine - Death - Burial Site?

Both the above letter and note are added to your journal. Keep going down the hall, and you will come across another mystery letter:

September 14th
Dear Mr. Barker,
Thank you for returning my inquiry regarding the Lilliane Shelley painting. It's wonderful to find another like minded collector, especially one that's so familiar with the early work of this local artist. I was, however, extremely disappointed that you have chosen to reject my offer to acquire this piece for my gallery. You have to understand that we are assembling what the Art Review has called "The most important and extensive collection" of Shelley's early oils ever displayed, and refusing to sell or lend the painting to the gallery is not only a disservice to Silent Hill, but an insult to the greater art community. Your refusal to support this celebration of Shelley's work will only lead to misfortune. I beg you to carefully reconsider my offer
Sincerely,
Melissa Matlan

Go back to the corridor, and through the door close to the entrance to the gallery, to find some stairs leading down. Go down the stairs, and explore the area. You will come across a room with a big table. This starts the quest: The Art collector and gives you your objective, to Find the Missing Paintings.

Examine the table. There are three paintings already on it. You need to find six more (See locations at the beginning of this tutorial), and arrange them together properly on the grid to solve this puzzle. This picture shows the paintings puzzle solution:

Silent Hill Downpour Painting Puzzle Answer

Use UV light beam from forensic flashlight on the new painting to uncover a secret map. Note: You can find a Forensic Flashlight in the trunk of a police car at the garage of the Centennial Building.

The map leads you to Monroe Cemetery, just SE of St. Maria's Monastery. Climb down a ladder in an open crypt. You now reach the Crypt Gate Tile Puzzle:

Crypt Tiles Puzzle Solution:
Press the tiles as follows:
Top Left
Center
Bottom Left
Bottom Right

Note: on easy difficulty, the first tile will already have been activated.

This solves the Crypt Gate puzzle.

The gate near the tile puzzle will open. You unlock the following achievement/trophy:

Art Appreciation
Completed the Art Collector Side Quest

Enter the burial room. Search the burial chamber for a first aid kit, box of shotgun shells, and a Tomahawk from one of the coffins, as a reward for completing this side quest.