I'd ask them about their friends. My grandma told me about her best friend as a little girl, and then what they would do for fun, and the stories just kept flowing. So I wouldn't bother asking anything too specific about the world around them, because (if they're like me) they'll just be like "Uh.. I dunno." But if you ask specifically about something like their favorite (or least favorite) teacher, then that would probably be a more effective way of doing it.
Also, one of my secrets for asking good questions: some people say not to ask a "yes no" or 1 word answer type question. I've personally found these to be okay, or even great, as long as they're followed up by a "why?" or a "so how did that influence you?"
Possible questions:
1) Who was your best friend when you were little? What did you like to do together? What's your best memory with them?
2) Where did you work for your first job? What did you do there? Who was your boss? How did you interact with him?
3) What is the best vacation that you ever went on as a kid? Why did you guys go there? What was the best part? What made it memorable?
4) Where did you guys live? Did you have your own room? Who did you share with, or did others in the family share?
5) What did your family used to do on Sundays? Did Mom make dinner? What was the best meal? What was your role in helping?
6) What are your hobbies nowadays? How did you get into it? What did you used to do for fun? Was anyone else in your family involved in it?
7) How did you feel when __________? What was life like for your during __________? Where were you when__________? (I was thinking more historical events, like the segregation, JFK's assassination, the Depression (if they're old enough) or the moon landing for these.)
8) Did you ever do any crazy things when you were a kid? What made you want to do that? Was it worth it? Do you regret it? Would you do it again?
9) Where was your dream house when you were little? Why did you want to live there?
10) What was the most important thing that ever happened to you? What is your defining characteristic? What makes you "you"? How did you develop that attribute?
Remember: these aren't questions you ask as a list. The ones that are grouped together could be in the same conversation, but throw in filler questions. Every one of these questions could benefit from a follow-up question of some sort. Meanwhile, be prepared to stray from your script. If Grandma Mico alludes to another story while telling you about her best friend, by all means, ask about the other story right away! You can come back to the friend later.
I would recommend not making it a formal interview, but making it more of a "oh hai grandma I just wanted to come over/call and chat" to avoid nerves.
Good luck! Sounds like fun! If you find any good stories, be sure to share.