My son didn't start playing with his 1st birthday toys (*really* play) until now and he's 2.5 years! He actually like the boxes and wrapping paper more. ha!
I think the classes idea is fun. Gymboree, or a swimming class is something you can do with her and she'll enjoy your company more than a toy.
That being said, some things 1 year olds might like: musical toys/noise makers (not electronic ones...shakers, drums, etc.), bubbles (a machine or something you blow for her), a special doll or stuffed animal, a tent or tunnel they can explore/crawl around. Anything that promotes more active exploration...
they don't really get "toys" in the imagination sense yet. I would wait until 2 or 3 years for those.