I think the setup is good for the most part. My only advice is not to ask them as a group. Have each individual tell you their backstory and reasons for being in jail separately. Once you know them all, you can have a lot more fun intertwining their plotlines together in ways that the players themselves might not think of. You can implement small expositions throughout the campaign to build suspense and let the bonds between the players and characters blossom naturally, rather than setting them up like stats. Players, especially new ones, love hearing their characters details and pasts worked into relevant plotlines. That's where the magic lives.

Where is this jail cell? What’s the city name, vibe, etc?

That's a bad question, because it draws blanks, not leaves them. Better questions would be:

• «Fighter, how big is the city? Is it more like a village, or something closer to a big, prosperous metropolis?»
• «Rogue, which known criminal is doing his time in some other part of this jail?»
• «Barbarian, you've been there quite a lot for your drunken fights, did you? Name one guard who's here now, you know each other a little too well!»
• «Wizard, for what breakthrough the local magical academy is known?»
• «Cleric, which religion do they preach here?», and, optionally, «Which part of it you would never agree with?»

Don't just ask «what's the city vibe», get them something to build from!