Bitterblue, by Kirstin Cashore, is a lovely example of a place-centered, political-intrigue-filled, character-driven fantasy. Bitterblue's city, with its three wondrous bridges leading to swampland, and her castle, with its strange art filling its halls and garden, are vividly described, and the book is set firmly in these two settings. Bitterblue's struggles to understand the reverberations of past atrocities in the politics of her present drive the plot, and Bitterblue herself--young, uncertain, lonely, determined, and just plain nice--is a lovely character (here's my review).
I was happy to host a publisher-sponsored giveaway of two copies of Bitterblue, and I encouraged entrants to leave (optional) recommendations for books that shared those three elements.
The two that occurred to me were King of Attolia, by Megan Whalen Turner, and Star Crossed, by Elizabeth Bunce, and I'd also add The King Commands, by Meg Burden, to that list (although it's not quite as one-place-eseque as I had in mind). Here's what was offered in the comments (thanks very much, all of you!), with my own thoughts in parens.:
Crown Duel by Sherwood Smith (especially the second half, Court Duel, and I would add to this Smith's Stranger to Command)
The Lumatere Chronicles books by Melina Marchetta (yes to these on politics and character, but I'm not sure these are tightly enough centered in one place--I'm looking for things that are more claustrophobic! Erin also recommend these...)
The Study series by Maria V. Snyder (definitely the first one has all three elements!)
The Nightrunner series by Lynn Flewelling (I've never read these, and have added them to my list!)
Meg S suggested Malinda Lo's books (Ash and Huntress); although I love these, they are not quite the political fantasy type of book I was thinking of!
Melissa at One Librarian's Book Reviews offered her whole list of Courtly Intrigue, and suggests Grave Mercy by Robin LaFevers (which is waiting for me downstairs next in the tbr line)
Michelle suggested two books I haven't read that sound fantastic--Seraphina by Rachel Hartman and Candlewax by C. Baily Sims
The False Prince (of course!), from Natalie (of Literary Rambles)
Theft of Swords, by Michael Sullivan (from KT)
From Katy (aka library-mama) comes Lois McMaster Bujold's The Curse of Chalion, and Girl of Fire and Thorns, by Rae Carson; from her husband the Steven Brust Taltos novels (I haven't read any of these!)
Chime, by Franny Billingsley, and Boneshaker, by Kate Milford were also mentioned, but I don't think either has the political intrigue I'm looking for...
and the winners of the two copies of Bitterblue are: KAREN and KATY!
More recommendations always welcome!