I'm not sure if you're still looking for answers, but here's what worked for us... We were having the same problem with our 6 year old being bored all the time. She likes art, so I set up an art center for her to be able to easily get art supplies in/out. We even converted our coat closet (by our front door) into a game/puzzle/large toys closet so the kiddos could get whatever they wanted on their own (yes, even at 6yrs. old). I went on to explain to her that if she played on her own (read, play in her room, did an art project, watch a movie, whatever) until lunchtime, I'd give her one hour after lunch of whatever she wanted to do with me (usually it's a board game). This has been working for us for quite some time now. Of course when there are errands to run, the hour of together time does not come into the picture. I also give her extra time for helping me do chores. I explained to her that when she helps me, it frees up more time for me to be with her. This also works (for the most part).
Our family also has 'Super Sunday Family Funday', where every Sunday is our fun day. Since we are on a very limited budget, we go to the $1 movie theater, the park, the mall to play, or any free/cheap events at museums and other local events. (I'm really good at finding great deals for local entertainment). It gives us something to look forward to each week.
I've read a few posts and I have to say that I don't think your child is doing this because she feels like she isn't getting enough of your time. I think she does these things because she's simply lonely. She is definitely old enough to get her own drinks - my 6yr old will get water with her cup in the bathroom on her own. I think it's just a matter of encouraging her interests and teaching her to be a little more independent. Maybe she could do something once a week, like gymnastics, dance, music, or perhaps a sport? Sometimes when my girl is bored, I just have her practice her gymnastics. She gets really excited about putting on her leotard because I don't let her do it often, except for class and when she's really bored. We either put on Bella Dancerella or she practices what she's learned at her gymnastics class. I highly recommend the dvd games that teach children stuff. There are all kinds of dance ones, but now they are even making karate ones, too. We have the karate one, as well as a few dance ones and they are a big hit in our house! Well, I hope this helps a little. Take care and good luck! ;0)