something like Code Geass or No 6 - futuristic rather than Sci-Fi

[FrejaOne]

Futuristic setting that looks "clean" and advanced (New Tokyo in CG, the model zone in No 6). Action, suspense and many mysteries. An element that seems paranormal rather than scientific. Stuff like that is appreciated. (Speaking of setting, I also loved the city in Madoka).
Darker than Black sort of fits, too, though its setting is different.

What I don't want is the space opera stuff: aliens, spacecraft, other planets, etc, and hardcore cyberpunk or virtual reality (like Ghost in the Shell or Dennou Coil).

Thanks in advance.

UPDATE: Found Guilty Crown with the help of some nice people, adding it here in case someone shares my request.

[SeijiSensei]

For clean, advanced, and futuristic, I'd suggest Ergo Proxy, though being out of print it is now ridiculously expensive. You might want to watch it via Amazon streaming. For a paranormal series, I'll recommend Ghost Hound.

[Kirito]

Give Sora wo Kakeru Shoujo a shot, it's a space setting anime, but it has the futuristic and Sci-Fi elements that you're looking for.

[Haak]

I recommend To Aru Majutsu no Index.

[FrejaOne]

Thank you.

I watched Ergo Proxy, forgot to add it to the list though it technically fits.

Also adding Asura Crying for those who follow this thread. I wasn't too fond of it, though.

I'd appreciate more suggestions.

[Haak]

You might be interested in Kino's Journey and Tiger & Bunny (especially the latter)

There's also UN-GO.

[Dawnstorm]

Hm, it doesn't have much action, suspense or anything supernatural, but you might want to check out Eve no Jikan (Time of Eve).

[synaesthetic]

Originally Posted by Deikan

Give Sora wo Kakeru Shoujo a shot, it's a space setting anime, but it has the futuristic and Sci-Fi elements that you're looking for.

n'thing this. Raygun Gothic 1950s WORLD OF TOMORROW style shit like nobody's business.

Also hilarious if you've watched a lot of mecha.

[Xenio]

Originally Posted by Haak

I recommend To Aru Majutsu no Index.

second this and recommend To Aru Kagaku no Railgun (A Certain Scientific Railgun), it have more Science than To Aru Majutsu no Index

Academy City is a highly developed place in terms of technology. It is said to be 20 to 30 years ahead of the rest of the world. 80% of its 2.3 million residents are students. The focus of studies here is directed towards esper powers. Misaka Mikoto, one of the top level espers in town, shares a room with Kuroko Shirai, another high level esper who is a member of Judgement, a law enforcing agency composed of students. Both attend to Tokiwadai, a private school reserved for the high-leveled and the rich. Kuroko's partner at Judgement, Kazari Uiharu, is a low level esper who studies at Sakugawa middle school. Her best friend and classmate there is Ruiko Saten, a level zero (no esper powers). Together, the four encounter several adventures in the exciting scientific town.

[Elegance]

Guilty Crown, basically like Code Geass

[Cosmic Eagle]

Seconding Index since it is one of the best ones that fit your criteria. Should try reading it too. The science is also more mystical occult than science...

[Kleo Scanti]

If you're in a mood for something peaceful, watch Aria the Animation and its sequels. Technically everything happens on another planet (terraformed Mars), but there are no aliens, if you don't count Martian cats as such. You will explore the city of Neo-Venezia (which is a replica of Venice) along with an apprentice Undine (gondolier) Akari and her friends. Some say this anime is too slow, because it's a Slice-Of-Life in its purest form. But I know people who only watched bloody action before, and then converted into Aria fans, so give it a try even if it's not your preferred genre.

[MisaoFan]

Horizon on the Middle of Nowhere - It's a advanced, futuristic space fantasy, however it sets mainly in a spaceship, but there's also the land as well. The story happens to be a futuristic version of Warring States and fits (?) your description.

Senki Zesshou Symphogear - Sets in the futuristic Japan, but there's an alien threat in it.

[SeijiSensei]

Let me toss out a couple of other suggestions I didn't think of the first time around.

One is Toshokan Sensou, set in a near-future period where librarians and censors have formed armies and fight over what people are allowed to read. It's better than the premise suggests and has a nice romance.

I'm also going to suggest Real Drive though it might have too much science-fiction for you. It's by the creator of GiTS and Ghost Hound, Shirow Masamune. It's a hard show to describe; here's the listing at ANN:

Originally Posted by ANN

Real Drive is a "neo-futuristic science-fiction suspense" story is set in A.D. 2061, when a new, more secure information network called the Material Network (or "Metal") has taken over human society. However, aberrations begin to crop up as individuals chafe against the rigid system, and so-called "cyber divers" are dispatched to investigate these incidents.