This page of The Last of Us game guide contains a walkthrough of the Safehouse stage as part of the Bill's Town chapter. This level involves fighting the monsters, although you will spend most of the time in the title hideout of Bill. In addition, Joel will get a shotgun and bombs, and will also be able to upgrade weapons.
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After the cutscene ends, search the area thoroughly. You can find a lot of useful items here that will come in hand throughout your journey.
After you are done, follow Bill to the first floor and explore this area also.
When you finally leave the building, you should get ready to fight off a group of enemies. The monsters will be coming from the right and there will be several clickers among them. Eliminate these ones in the first place.
As soon as the area is clear, follow Bill. The man will take you to the stairs leading to a warehouse.
After the cutscene ends, explore the ground floor of the building thoroughly. You can find here a lot of tools and useful materials, as well as the first level of tools.
Thanks to these, you will be able to craft weapon upgrades on the nearby workbench.
You will also receive a shotgun, and a bomb from Bill. The former is perfect at short distance and the latter can be used instead of the Molotov's cocktail, or set in places where you expect the enemies to walk.
Once you are done with exploration, follow your companion upstairs. The man will take you to the big stained-glass windows and opens one of them. Before you move on, it is a good idea to check out Bill's office to the right.