DD just turned 1 last week, and it was like a switch went off in her head. She, seemingly suddenly, can do toddler activities, play with toys "the right way", and not put *everything* in her mouth. Since no one else responded, I'll tell you what new stuff we've been doing. (I'm no expert).
Drawing. I bought a magnetic drawer until she graduates to jumbo crayons. I'm tired of the tantrums from pulling crayons and markers out of her mouth.
Blocks. I like the mega bloks, but then DD pushes down on regular blocks to try to get them to snap.=)
Water outside. Buckets, tupperware, spoons, I work the hose.
Dancing, chasing, conga line. DD says "dada, dada, da, DA!" with me.
Tasting food. Really helpful for me. Now, she can sit in her high chair in the kitchen and "eat" while I cook.
Toddler toys. Peg puzzles, shape sorter, ring stacking toy, nesting toy,
Helping with chores. DD will hold a rag while I wipe the floors, or hold the dustpan while I sweep.
Music time. I bought the band in a box by Melissa and Doug. It's pretty crappy, but DD loves it and it was an easy purchase for me. She can do all the instruments herself except hold the triangle by the string. Or we just listen to music and dance.
I have yet to let her run around outside and explore nature too much. When we're outside, I'll bring her bricks, large rocks, potted plant, etc.
And of course we still do the baby stuff that we were doing before, like swimming, library storytime, playdates, reading. I'm excited to share because it's been fun for me. Really, so many new things all of a sudden.