Two that spring to mind are MASH and Gilligan’s Island.

Mike Brady on The Brady Bunch. But he did a fantastic job!

Mike Brady on The Brady Bunch. But he did a fantastic job!

I don't think that fits since I'm talking about characters. Robert Reed may not have wanted to be there, but Mike Brady certainly was happy in his situation.

Another example is Taxi. Most of the characters didn't want to be working at the cab company.

There were many times that Mr. Wilson didn't want to be anywhere near Dennis.
Uncle Martin would rather be home on Mars than living with Tim.
Sgt. Carter often times didn't want to be near Gomer.
Lisa Douglass didn't want to live in Hooterville.
Granny didn't want to live in Beverly Hills and Mrs. Drysdale didn't want to be near The Clampetts.
I think that Alf wanted to be back home in Melmac.
Fish wanted to be away from the foster kids.

Lisa Douglas didn't want to live in Hooterville.Only for the first few episodes. Lisa ended up being a lot happier than Oliver in Hooterville.

Only for the first few episodes. Lisa ended up being a lot happier than Oliver in Hooterville.

I often wondered if she just gave in and learned to live with it. The character had a forgiving way about her. She did truly get along with everyone which made the acceptance of needing to be there that much more tolerable.

It's About Time
Lost in Space (well it sort of became a sitcom)
Dusty's Trail
Josie and the Pussycats in Outer Space

Do you thing the mother from My Mother the Car wanted to be cooped up in a 1926 Porter when she could have been reincarnated into a Mustang or a Corvette?

You could say the McHale's Navy guys, but most of the time it didn't seem that way.

Most of the time it didn't seem like Rhoda wanted to be in Minneapolis. Probably so, since she moved back to New York after a few years.