On story and believable characters, you can't really beat [url="http://www.gog.com/en/gamecard/fallout"]Fallout[/url] (specially the [url="http://www.gog.com/en/gamecard/fallout_2"]second[/url] one), or [url="http://www.gog.com/en/gamecard/arcanum_of_steamworks_and_magick_obscura"]Arcanum[/url], which I always considered kind of a spiritual sucessor, even though it has nothing in common with the Fallouts, other than being done by largely the same developing team, being turn-based (or, rather, having the option of enabling turn-based play, which I highly reccomend) and having the same quirky sense of humour, interesting characters and a great storyline (which is already more than Fallout 3 has, but that's nor here nor there)
Look, I know not many people will reccomend these, since they are considered pretty sandboxy. These people are wrong. Dead wrong. So wrong it hurts. Arcanum has what is, to my liking, the best fantasy setting in a videogame, bar [url="http://www.gog.com/en/gamecard/planescape_torment"]Planescape[/url]. And the story is top notch stuff. Real great storytelling, unlike what Bioware passes for cinematic experiences these days. Fallout... Well, Fallout is Fallout. I don't think I have to explain that one. Buy these games. Play these games. Enjoy these games. No need to thank me.
Also, if you don't mind getting a little shootery, [url="http://store.steampowered.com/agecheck/app/34010/"]Alpha Protocol[/url] has a pretty enjoyable storyline, and a quite nuanced take on characters and personality, that I wish was explored further (it gives Bioware's conversation wheel a purpose! And it finally makes the character influence thing that Obsidian is so hell-bent on implementing make sense! What more could you ask for?). It's somewhat open-ended, so it should fit the bill, but there are people who LOATHE the gameplay. I quite liked it, but, you know, approach with caution.