Before I start playing a game I like to do some research but I can't find..

During the whole year, then? (:

Nami's most favorite item is gratin. Her other favorites include grapes, red magicgrass flowers, every season sun, chocolate or stew. She also likes, though not as much, fish, emeralds, wine or ketchup. Deciding when to give her those items will depend on what you have available at the moment, don't worry about it too much.

In case you're planning on giving her gratin, you'll need an oven and the following ingredients:
- onion;
- butter;
- milk;
- cheese;
- flour.

Hope this helps! For more details, go here:

http://www.fogu.com/hm6/chan3/nami.php

Also, an item the she likes is your dog ball. It raises her points by 300. Thomas gives you a new one everyday, saying you might've 'lost' you old one, so it's a free way to earn her love. But if given the option, go for gratin because the raises your love a lot more. Something I give to her (because I don't have a kitchen) are wild grapes found in Summer.
In Fall, you'll find the Red Magicgrass flowers, which she likes too. All year round you can give her Grape Juice, which you can either make yourself or buy from Karen, over the telephone.