I've found that my toddler really loves to do stuff together, anything really, one on one like you describe: Changing a light bulb is a major event, doing dishes, sweeping, really anything she can help with or be a part of is a lot of fun for her.
Something we did a few weekends ago that I will be repeating: We went to a local thrift store and bought a bunch of old magazines and books with lots of pictures. Looked and read through them together, cut out our favorites (mostly from magazines, like old Nat Geo's because we can re-read the books), glued them to the back of some upcycled cardboard, and finally hot glued a couple of magnets to the back and put them on the fridge.
~$5 for a couple hours worth of fun, high quality time together. Got to practice reading, identifying animals and nature, practiced cutting and gluing. It was great.
