If I am near an ocean, I always want to go to the beach no matter the weather. There are hikes, restaurants, tide pools and nature-center type places you can enjoy even on cold days.
If you do not have a car, maybe you do not want to mess with renting one for the day or using a ride share, but that would be my first choice, even in the winter.
If you just wanted to stay in the immediate area, you could really focus on the offerings right there like tours, classes and movies at the
Disneyland Resort Hotels. There’s also live music around Downtown Disney, and I’m currently seeing some Lunar New Year entertainment on the schedule at the Grand Californian. Unfortunately, I cannot see race weekend particulars right now.
You could also do a fun character breakfast, have a good dinner at a place like Din Tai Fung or do a self directed “food tour” with small plates, drinks and desserts at different spots around Downtown Disney District.
If there are fireworks in the evenings of your non-park days, you can watch them from the Esplanade or other spots for free.