Its easy to find karen in these places:
Morning - sitting on bench next to rick.
day-ish. - go inside the store, she sometimes dissapears for a few hours randomly, i dunno where she goes.
night - really late at night (

she goes to the beach, on certain days (i believe the days when the store is closed) she goes to the bar.
Birthday »
Fall 15 (alt Fa 23) (alternate only happens if you picked fall for your birthday)
Special Foods » (you have to be able to create these in your kitchen... buying them eats them immediately)
Pizza, French Fries, Popcorn
Favorite Foods »
Cheese, Wine, Truffles, Tempura, Sashimi, Bamboo Shoots, Pink Diamonds, Diamonds, Perfume
Wine is probably the best bet, buy it from the wine-cellar every day and give it to her. Sashimi is also very easy to get. Fish, then use Fish + knife in your kitchen (perhaps some soy-sauce for seasoning) Bamboo shoots will hold throughout spring, and Im suggest giving her grapes in the fall. But, always try to get her WINE. she's an alchoholic. Pink diamonds and diamonds are found mining, very low levels, hard to get. Truffles require befriending the priest.. and perfume is only possible to get at the horse races, it costs 150 medals.
There are certain flowers she doesn't like, you have to judge by her reaction. I suggest you do the usual, talk to her twice, give her an item. Try to do this every day.
I know that karen does NOT like sweets, which is odd. Most of the girls love Eggs as well, thats how i won the heart of popuri =p.
Anyway, hope this helps..
What color is her heart?