The book you’re remembering is the second volume of J. B. Stephens’ post-apocalyptic young-adult series The Big Empty – specifically

• Paradise City (2005) – while several of the scenes you cite come from the opening volume, The Big Empty (2004).
(The series continues with Desolation Angels, 2006, and No Exit, 2007.)

Why it matches the scenes you recall

1. The walled town and escape through the sewers (The Big Empty)
   • Seven teen survivors (Jackson, “Maggie”/Magda, Clementine, Isaac, Jon, Daisy and Ronnie) are living in the strictly run settlement of Founders.
   • After discovering how authoritarian the town really is they break out by way of the storm-sewer tunnels, having a fierce argument about whether to leave behind a fever-ridden companion in the infirmary.
   • Founders immediately sends an armed “search party”, including a “gung-ho” guard, after the runaways; the pursuit in the forest splits the teens into a group of three and a group of two. Their agreed-on rendez-vous point is Salt Lake City.

2. Thanksgiving dinner in a cave (Paradise City)
   • The trio (Jackson, Jon and Clementine) hole up in a shallow cave. Jon insists on celebrating “Thanksgiving”, roasting a small game bird as the centre-piece. Clementine enjoys it, but worries that they have used up badly needed food.

3. Biker / bandit gang living in an abandoned zoo (Paradise City)
   • The three are captured on the road by a motorcycle gang that has taken over an old zoo.
   • Their leader styles himself a king; most of the animals have already been eaten.
   • He orders the two boys fed to the alligators and keeps Clementine to be a concubine; slave girls dress her in make-up and new clothes while one warns her: “When he enters you, don’t cry – he hates that.”

4. The “Peacekeeper” in Salt Lake City (Paradise City)
   • The other pair of fugitives (Isaac and Daisy) make it to the outskirts of Salt Lake City.
   • A uniformed federal “Peacekeeper” asks why they’re not in school and demands their travel papers / passports.
   • Isaac improvises, claiming they are recently engaged and travelling to meet family; the Peacekeeper lets them go with a sympathetic warning.

Setting & background
A mysterious plague (“Strain 7”) has depopulated North America. Isolated towns have walled themselves off, fuel and food are scarce, the central government’s only presence is small Peacekeeper detachments, and lawless gangs roam the countryside – all exactly as you describe.

So the series you want is The Big Empty by J. B. Stephens, chiefly the first two volumes, The Big Empty and Paradise City.