Most the cast is around 16-18 years old. The oldest out of the Future Gadget Lab members is Moeka Kiryuu who's 20 years old.

Paradise Kiss, Koi Kaze, Princess Jellyfish, Emma, Hanasaku Iroha, Genshiken, Strawberry Marshmallow, Kanamemo, Chocotto Sister are some of the series I've seen which would fit the bill.

I got to thinking, even though the characters from The Pet Girl of Sakurasou are in high school, the entire show reminds me more of the lives of people in college. I mean they are living in a dorm and most of their worries have to do with their goals for a professional life rather than high school related stuff.

I'd say Steins;gate doesn't fit the bill because it's not slice of life.

It is actually. A Slice of Life show that is. Not fully, but that type of genre is present in the show, as well as the VN.

Kokoro Toshokan ... has nothing to do with school as I remember, but I dont think theres any romance in it (been ages since I watched it). It's an extremely slow moving show. Think of Aqua and then think of Aqua on sedatives and you have Kokoro's Library lol.

Usagi Drop is the one that comes to mind first.... Welcome to the NHK, there is another.

Genshiken is my favorite. Aleast one person mentioned it.

Honey and Clover. The Aria series (the one with the Gondolas that takes place on Mars).

Nodame Cantabile and Space Brothers are pretty ultimate for post high school slice of life.

Those exist? Gasp!
I kid, though I honestly can't think of a single one which hasn't already been recommended, many of which are being repeated anyway, so I guess they are just as few in numbers as I assume they are.

Nodame Cantabile is a good one about students in a music university.

Honey and Clover is a pretty decent one about students in an art university.

Skip Beat! It's about a girl who becomes an actress to get revenge. I thought this one was really funny too.

Kino's Journey. It's about a traveler who goes on a journey from town to town. Think of something like Star Trek where each town represents a certain mindset or ideology. Not much in terms of romance though, unless you're talking about Romanticism, then it's all about the journey and not the destination.

Galaxy Express 999. Like Kino's Journey but sci-fi. It's about a boy who boards a space train to go to the Andromeda Galaxy to get a mechanical body. He travels with a woman named Maetel. If you don't have time for 113 episodes, there's a movie that covers the major plot points, but I like the weirdness and melancholy aspects of the episodes too. It's a 70s anime/Leiji Matsumoto story so it looks very different.

Durarara! It's a pretty fun anime. A lot of characters and plot threads but I Iike how they were interwoven together and told a bigger story.

Michiko to Hatchin. It... kinda reminds me of Les Miserables but a lot more fun. It's kinda got a Cowboy Bebop vibe to it. It's about a woman, Michiko, who kidnaps/helps this girl named Hatchin to find her father, who is Michiko's lover. There's a lot of action.

Gosick. About a girl named Victorique who is Sherlock Holmes. They're high schoolers but the focus is on mysteries.

Spice and Wolf. About a peddler named Lawrence who meets a wolf god. It tells stories through the lens of economic concepts like currency trading, the stock market, supply and demand, and contracts.

I second Princess Jellyfish, that was pretty good. Hanasaku Iroha has a bunch of high school girls, but it does focus more on the Japanese inn they work at and the history of the inn.

Ai Yori Aoshi is romance/slice of life, with mostly college age characters, and hasn't been mentioned yet. Wagnaria! is slice of life, quite hilarious, and while some of the cast is of high school age, most of what you see relating to school involves them studying in the break room. Polar Bear Cafe is also worth mentioning.

You could try Planetes. Not one of my favorites, but it might fit what you're looking for, but with a (realistic) sci-fi basis.