My daughter is about the same age as your child, almost 2.
It is tough to entertain them.
She does 1 class a day (which lasts an hour) except Friday and Sundays. These are: a dance class, a music class, a sing a long, rhyme time. Most we pay for, but rhyme time is free at the local library. We often do long walks, bus rides, errands, letting her loose at playgrounds (which fortunately are not overrun by older kids) or even shopping centers. We live in London, so I am not sure this helps you too much.