hoping to meet your criterion of good and non-accessible up north:
shanxi: lao xi noodle house (arcadia). everything there is good, but pay particular attention to anything described as a "house special" or "wife special" dish
shaanxi: xi'an tasty, (monterey park) liang's is more pan-chinese (including shaanxi) but also makes some of the best noodles in the SGV. try the lamb noodle soup.
two other places known for the noodles include: dao shaw/heavy noodling II in the JTYH plaza, and kam hong garden (which might be a good choice since beijing pie house is in the same parking lot - i like the pie with pork/fennel)
shanghai: i personally favor places like shanghai dumpling house, shanghai bistro which are more bistro type fare than restaurant fare. love the chicken & chestnuts at shanghai restaurant in focus plaza.
tianjian: i think the tianjian bao are better at tianjian bistro, but that and maybe the meat pie are the only things worth getting there. OTOH fortune no 1 has the better breakfast including the fried bread covered in cinnamon. and the fried crispy something wrapped in an egg crepe.
if you don't have burmese, try yoma myanmar in monterey park. they're worth a try IMO.
sadly, no fujian to speak of.
we allegedly have the market cornered on wuhan cuisine, but i find it kinda meh myself. a chacon son gout.
anhui: we have a place recently opened. can't vouch for it: china tasty
dalian: tasty noodle house. they also make a pretty good shui jian bao.
beijing: we have a few places, but none i'd recommend
dongbei: my favorite (shen yang) closed recently. you might try chef geng