Games games and more games. Go to a garage sale, or good will, and pick up clothes to do dress up (my 4 year old loooves dressing up).
Find out what are her favorite shows and movies. My kids like TV (my son will watch it any chance he's got, my daughter could care less about the TV) but they both have a lot more fun re-enacting the show or movie than watching it. Example is, my son LOVES Ben 10, but he is mildly-severely autistic, and he just cannot handle the show too well (turns around hitting his sister, kicking her, every time). So, we went to the store and bought him his own Ben 10 watch. He's yet to complain about not watching the show, and plays with it all the time.
If anything, something to break the ice, go to the store and buy Hullabaloo DVD edition. It's a game put out by Cranium. You get little pads of animals, you spread them on the floor, pop the DVD in, and watch the TV and he will tell you what to do. Might break the ice for her to let her play more games with you, while also 'watching tv' at the same time. My kids love the game. It gets them up, and active, and they get to act silly and have an imagination.
Go outside with her. If she's not interested, make it interesting. Buy some bubbles and blow bubbles with her (I don't know a kid who can resist wanting to blow bubbles). Buy some chalk and draw on the sidewalk with her. Play tag between you and her. If you've got leaves on the ground, pile them up and let her jump into them.
Holiday ideas? Let her help you with everything. Make some cookies, and let her help you, and as a reward let her eat some cookie dough. Let her decorate them if you've got sprinkles. When Christmas comes, let her help you decide where the ornaments should go, all the while playing x-mas music.
Look in the phone book and see if there are any toy domes around where you live, like a Chuck-E.-Cheese, and take her there for a day. There is a place where we live, where it was filled with a whole bunch of toys and physical activities (for babies on up) and their parents could interact and play with (and in) too. It was called something like Play Time or something similar. Both of my kids played so hard, they went to bed so early that night and slept the whole night through, and begged to go back there again.
First things first is to break the ice. Me and my kids play a lot of board and card games together. Maybe next time you go to the store with her, take her to the board game isle, and see what she looks at the most. Even if the game is too advanced, you can always change the rules until she is older to play it the right way (have to do it for my son a lot). If you can find a pack of Go Fish cards, that would work well too. That was the first card game I introduced my kids too, and they caught on real fast (my daughter was 3 then too).