Some good activities for a 16 monther are:
1. start teaching them how to follow a simple obstacle course. She can help you set up by moving pillows, pushing chairs etc. Then show her how to go over things, under, through around etc. Also jumping on the couch cushions on the floor and making a cubby house is fun. My son liked to just knock over all the cushions at this age but setting it up, pushing and pulling them then jumping on them used up some energy.
2. Take a tram ride. My 3 year old did it yesterday for the first time and loved it.
3. You can still take them shopping and have her push the cart while you steer.
4. finger painting with shaving foam
5. playing in water either on the kitchen floor or bathroom