I call my grandparents Nanny and Papa. It just sounds right to me.
Ah! You got to Yia Yia before I could. My cousins are Greek, and their grandma was born in Greece so they used this. They pronounced it “ya” like a short “yeah,” though.
As others have pointed out the kid(s) might choose their own names for you, and each one might choose something different. For example my cousin called my grandfather “Bumpa” because Grandpa was too hard for her to say.
You’ll find it adorable, I’m sure, whatever they choose to call you.
Those are pronounced “BOB-cha” and “BAH-chee” to you non-Poles.
As Hal said, my daughter calls my MIL Baci (BAH-chee).
People I work with are Nana, Mawmaw, Mima (me-ma), and of course, Grandma. How about one of those variations?
Grandmere and Grandpere. No, we’re not French but my grandmother sure wanted us to be!
My dad is Boompa, after James Stewart in Mr. Hobbs Takes a Vacation.
I called one of my grandmothers “Mama” (as all her grandchildren did), and the other “Bigma.”
I go by Babsie and my husband is Papa Bear to the grandkids. Our daughter-in-law named us and I love to hear one say "I love you, Babsie. " Other names in the extended family are MamMaw, Gee-pa, Ninna, Big Pop, Omi, Oma, Opa, and Grandaddy.
I suggest “The Boss”.
Maternal grandparents: Grandmother (sometimes Granny) and Grandaddy
Paternal grandparents: Mama[lastname] and Pop
My stepchildren call their grandparents MeeMommy and Deedaddy; I think that’s kinda cute.
Nothing I’ll add is original I don’t think. My kids always call my parents Gramma and Grampa, but my older son referred to his first day-care provider and her husband who were older than my parents Mima Phyllis and Pepa Dick (both long e sounds). I thought that was cute.
We also had a Bumpa, but that was only for my maternal grandfather. The other one was Grampa Wilford.
What is “Busha” or “Busia” (I don’t knowhow to spell it)? My mom called her Polish grandmother that, and I was planning on having my kids call my mom that. Is that not real Polish?
I’m a Southern boy, so I called the grandmother I saw every day “Grandma” and the one I saw every so often “Grandma Lastname.” My grandfather’s second wife was “Grandma Firstname.”
My remaining grandmother is now just Grandma. Both of them were Grandma Lastname if I needed to specify which Grandma I was talking to/about/whatever.
I am still highly amused that my mom’s paternal grandmother, who was known by all as Grandmother, refused to let any of us call her Great-Grandmother because it would make her feel old. She was 75 when I was born. She was definitely old. But she also was the family matriarch, so Grandmother it was, because that’s what she liked!
I call my grandmother “Nan”, which doesn’t seem too country-bumpkin to me. My husband’s grandmother is “Grandma”, which does, but of course she’s from the country.
I will have to back up Dangerosa (in a less issue-laden manner 
) about the whole “just give up trying to disguise the fact that you’re a grandmother” thing, though. My step-mother, in her mid-40s, kind of freaked out when my younger step-sister had her first, and went through a number of names before settling on “Bubbi”. The search and the resulting name just made her look silly. Unless you plan on denying the fact that they’re your grandchild, people will think more about whatever strange name you come up with than they would with plain old “Grandmom”.
French-Egyptian friends call their grandmother ‘Mehmeh’ and grandfather ‘Nunu’. I have no idea how you’d spell that. Their daughter-in-law is called Nona by her first grandchild.
I called my grandmothers Bubby and Baba, two regional variations on Yiddish for Grandmother, but you’ve already rejected those. My Bubby, who had many grandchildren, was actually ‘Grandma’ to the eldest few, ‘Savta’ (Hebrew for grandmother; ‘Saba’ is grandfather) to the Israeli grandkids, and Bubby to the rest of us. I suppose after raising thirteen kids, she had to be a flexible person.
Let’s see:
Mother’s Mother is Meme. It was what I could say as a baby, I guess. All of the grandchildren (and some neighborhood kids) that came along after me also used this.
Mother’s Grandmother is Nanny. My uncle started this one as a kid; it stuck. Everyone still calls her this–she’s 96 and he’s in his 50’s.
Father’s Mother is Grandma, sometimes Grandma lastname for clarity.
Father’s Grandmother was Grandma firstname or just firstname. She was not a nice person.
Step-father’s Mother has been Grammy at least since my (half) sister was born. I don’t remember what I called her before that.
Step-father’s Grandma was Gramma Dolly. Dolly was a nickname that everyone called her. I don’t know if I know what her actual name was.
one of mine was “mother-first name”, the other was "grandmama-last name. if i ever have grandkids, i think i’d like the “mother-first name”. of course, if your first name is teresa, it might be a little pretentious! i think a lot of kids end up calling their grandparents whatever they themselves come up with.
I’m 38, and I want to age gracefully. To me that means not being coy about my age or admitting I have grandchildren or whatever. I’ll be a “Grandma”.
Besides, all the cutesy alternatives just make my skin crawl. (Sorry, Papa, you know I didn’t mean you.)
My maternal grandmother was Grandmother. My paternal grandmother was Grandma. My niece and nephew call my mother-in-law Nana.
For what it’s worth, my brother and I called our maternal grandmother “Grammarie” when we were kids. (We’ve picked up her great-grandkids’ habit of calling her “Gramma” or “Gammy” now.) Of course, unless your first name happens to also be “Marie”, that won’t likely help. 
The distribution of the word “baba” fascinates me. I didn’t know it was Macedonian for Grandmother, but I knew about the similar “babcia” in Polish. I believe “baba” also means “grandmother” or “old woman” in Russian, and I know it means “old woman” (or, more rudely, “old hag”) in Japanese. Some of the uses likely share roots, but in others I suspect it derives from the process of language acquisition in children, similar to parallels in the use of “mama” and “papa” in several widely separately languages.