I know how it goes. Things that have worked for me with my niece and her best friend:
Taking them to a movie. Not super quality time, but frequently it's the only compromise available when the 6 year old nephew is along. I earned points for taking them to High School Musical 3 (truly awful) and Twilight (awful but hilariously so).
Zoo/aquarium. I was surprised by how high the animals scored with the girls. I thought this might be something they were too cool for, so it was a pleasant surprise.
Taking them out for sushi. This was ultra cool to them and scored me many "cool uncle" points.
Taking them to a tapas joint. They were lukewarm until I taught them how "tapas bar" sounds a lot like "topless bar." I then had to teach them what a topless bar was, but once they got the idea, the whiff of scandal delighted them and suddenly tapas was cool.
Theo chocolate factory tour. This was only OK, by their standards.
Taking them shopping. At first I thought this idea would be a surrender, but I managed to turn it around (for me - they were into it from the get-go). I basically took the opportunity to talk to them about the things they wanted, how much they cost, shopping sale items, what things they might want to save up for, etc. When my sister told me that my niece bought an entire school year's clothes and came in more than a hundred bucks under budget, I figured our mall discussion had come in handy.
Teaching them to drive something. My sister rented a wave runner (basically an aquatic motorcycle), and I taught them how to drive it (illegally), and turned my niece's mild-mannered, sweet, retiring best friend into a complete speed demon terror on the lake.
Something that wasn't such a big hit: Camlann Village, where we had dinner at the medieval Boar's Hede Inn. I was pretty sure it wouldn't go over well, but my sister charged ahead with it. My niece and her two friends were totally disrespectful, constantly mocked the poor dude who was playing the lute and singing, mercilessly tore into his goofy british accent, and asked him if they sold condoms when they went to the bathroom. In other words, they were almost as charming as my sister and I were at that age ;-)
Good luck, and if you find any other good activities, let us know! Unclin' ain't easy.