Season 1 - Numbers

Santa Rosa Mental Health Institute is located in California where Hurley was a patient at one time for his eating disorder.  SRMHI also has connections with other characters in the show.  John Locke's biological mother was institutionalized there as well as Libby.

In S1E18: Numbers, Hurley goes to SRMHI to visit Lenny, a patient who has connections with the numbers.  

In S1E19: Deus ex Machina, Emily Locke's  admission papers to SRMHI were shown.  She was apparently suffering from schizophrenia and self admitted herself into the hospital.

In S2E18: Dave, Hurley's flashback is during his time spent at SRMHI.  At the end of the episode we also see that Libby was a patient there also.

Employees of SRMHI:

• Dr. Brooks
• Nurse Lazenby
• Dr. Curtis
  

Patients:

• Hurley
• Lenny Simms
• Libby
• Marcus
  

In S1E18: Numbers, Hurley is shown in flashback wearing a uniform and eating chicken.  Though Mr. Clucks isn't directly referenced, this is our first glimpse of the fictional fast-food enterprise.

In S2E1: Man of Science, Man of Faith, Hurley tells Jack about the "chicken joint" he worked at which got hit by a meteor, blaming it on his supposed curse after winning the lottery playing the cursed numbers seen on the hatch.

In S2E4: Everybody Hates Hugo, we actually see Hurley in flashback working at Mr. Clucks behind the counter.  His boss is Randy, whom we've also seen working at the box company with Locke.  We learn their slogan is 'Have a Cluckety, Cluck, Cluck Day".  After being accused of eating chicken on the job, Hurley, who's already won the lottery, tells Randy that he quits.

In S2E18: Dave, Hurley mentions working at Mr. Clucks.

In S3E10: Tricia Tanaka is Dead, during a news interview, we learn Hurley had bought a Mr. Clucks franchise and was preparing for the grand opening in Diamond Bar (a suburb of LA), along with his new employee and former boss Randy.  As the news crew goes inside to shoot some footage, a meteorite falls from the sky a destroys the new Mr. Clucks killing the newscaster Tricia Tanaka and her cameraman.

The footage for the scene was shot in Hawaii using a real life fast food chicken franchise called Popeyes.  You can also visit a website set up for fictional Mr. Clucks.