I'd prefer as close to a real-life Japanese Middle or high school setting as possible.
Well I looked through some anime I watched and came up with this suggestions in order from most recommended to least (all of them have no or little unreal elements, if yes they will be noted):
Gin no Saji - Great story about agricultural high school and students learning about bacteria, farming, shoveling muck, animals and such. Pretty hot-blooded shounen with some relationships and character development
.
Kareshi Kanojo no Jijou - A great romance story between two characters (no harems here), and generally a classic anime show with high school setting.
Sakamichi no Apollon - A high school setting, heavy focus on music - jazz, but its set in Showa era if I remember correctly (think 30-40 years ago).
After this mostly realistic shows with focus on drama/personal development, we can have some lighthearted comedies or shows that have some kind of supernatural element:
Great Teacher Onizuka - A classic story about a new teacher in high school (former delinquent) who tries to help his students with his unique style. A great comedy with really serious moments, also it is running most of the time on Rule of cool so it isn't really authentic japanese high school experience
.
School Rumble - Greatest love comedy from high school ever written (for me), it deals with lovestruck characters and their (sometimes very) misaligned affections. Also sometimes running on Rule of cool (one of the main characters is an alien - for laughs mainly).
Minami-ke - Greatest non-love school comedy - episodic in nature, but focuses on lives of 3 sisters and their daily struggle with the world
.
K-On! - If you want a perspective from all-girls school club, with focus on playing music (but mainly eating cookies and doing nothing), this is the slice of life of them all. I hate myself for recommending it
.
EDIT:
As Reelya says, Genshiken is still recommended, but outside your defined school range. I misremembered that it started in high school. And changed K-On! category
.