Some cute nicknames to consider are MeeMaw, GG, Gigi, Gammie and NeeNee. The choice can be largely affected by region, culture, or family history, and the grandmother in question should probably be consulted on the name before the decision is made.
There are many factors to consider in choosing a grandmother's nickname, but the choice can be a organic one. Basing the name on regional heritage may help. Meemaw, Nannie and MawMaw are typically Southern nicknames.
If a more cultural nickname is sought then Abuela is a Spanish term for grandmother. Babcia is polish, Bube is Yiddish, Lola is Filipino, Nai Nai is Chinese, and Nonna is Italian. Family history may be taken into consideration, as there are often family nicknames that are passed down from one generation to the next as a sort of spoken family heirloom. More modern names are in demand, leading to the creation of GG, GaGa, Ginja, Gidjet, Glammy, Glammama, Momsy, Geezergirl, MoMar, YaYo, G-mom and Pebbles. Ease of speech is another factor to take into consideration, as the grandmother may want the nickname to be something a grandchild can say with little frustration such as Shugah or CiCi, often focusing on strong vowel sounds for inspiration.