Check your local library for passes to local museums and other events. Check FB for local parent groups too. They always have the best lists of local places for each age. Look for soft plays, toddler gyms, mom and me classes, and zoos. If you post your city, maybe someone will have recommendations!
I know you mentioned libraries for morning, but we enjoy hanging out there in the afternoon. Nearby indoor museum (whether buying a pass is feasible or pass from library, as mentioned by someone else). Petco or PetSmart (we can spend FOREVER looking at the various animals in there lol). I get mine involved in things around the house - "organizing" pantry items, sweeping, folding (which takes 20x longer haha!). We also bundle up and still do walks, parks, etc.
Go to a McDonald's or other indoor playground. Not for the food, just so she can play.