Of all author's manga I only read Mio's Diary so far. Considering it's 4koma I guess this is a side series in the universe. What is the main-type one?
The main series is Sansha Sanyo, which is also a 4Koma manga. Most of Arai Cherry's works are "slice of life" so there is no plot development or something big happening with the characters from other manga besides getting to know them better. Here is the connections:
1. Mio's diary and Yuka Nisshi are one single ""story"" from a different character's perspective each. The restaurant where Katsuki works is the same place Odagiri Futaba and Tsuji Hajime (both from sansha sanyo) have eating contests.
2.Happy trails tells the story about Yasuda Takara and her friends. She attends the same school as Katsuki(Yuka and Mio's brother) and Tsuji hajime. She is also responsible for teaching Mio about Money.
3.Seinaru Megumi is a manga about one of Yoko's (Main character in Sansha sanyo) childhood friends, Osakabe sei. She even appears in the Sansha sanyo anime (ep 12).
4.Ichigo no haitta soda sui is set in Mannenrou academy, Yoko's former school before she went poor. One of her former friends is still there and has a secondary/tertiary character role.
And I guess that's it. Her other works are independent stories with different settings (Wonderful days, Tsunagumono, Mikakunin, Itsuka mata kaeru, Musunde tsunaide) leaning more towards fantasy/paranormal stuff but still focusing on their own slice of life part more than developing a "plot".
tl/dr: Sansha sanyo is the core work for more than half her manga but you do not need to read one to understand another.