Some of the most fun things for my toddler was simple things like going for walks at her pace, letting her look at nature and us talking about things. Cooking and cleaning were "fun" as she would handle the objects, and attempt to mimic what I was doing.
It is cold outside, but playgrounds, of course are always fun. If one is in walking distance, the biggest fun can be just walking to and from the playground.
Pretend play with dolls, cars, and villages. Putting down open umbrellas and covering chairs with sheets to make tents, "houses", etc... building "campfires" with blocks... These were things my daughters loved more than anything.
Reading to her. I think she would've sat for hours with me reading to her if I could have stood it. She also loved the library, and the children's section of large book stores.
Feeding ducks and geese out at ponds.
Visting with slightly older children who could talk with her and pretend play (she was an absolute chatter box after turning a year old), or having them come over to play with her.
Going to pet stores was always a wonderful diversion. And the bread store. Yummy.
Again it is too cold now, but in warmer weather I would bicycle with her in the neighborhood. And gardening. That was another thing she could do for hours as long as the weather was nice enough.
On the side of things we could not do as often - going to the children's museum, oh, and she loved the airplane museum (at the airport).