Here are a few ideas for indoor rainy day activities for kids aged 3:

1. Have a dance party: Put on some fun music and let your child dance and move around to burn off some energy.

2. Do a puzzle or play with building toys: Puzzles and building toys can help improve your child's problem-solving skills and hand-eye coordination.

3. Have a tea party: Set up a small table and chairs, and let your child invite their stuffed animals or dolls to a tea party. You can even make some pretend tea or juice to serve.

4. Do some arts and crafts: Cut out shapes from construction paper and help your child make a collage or picture. You can also try doing some finger painting or play dough sculpting.

5. Have a indoor picnic: Spread out a blanket in your living room and have a picnic with your child. You can even make some simple sandwiches or snacks to enjoy.

6. Play dress-up: Encourage your child to use their imagination and dress up in different costumes. They can be a superhero, a princess, or anything else they can think of.

7. Have a story time: Choose some of your child's favorite books and take turns reading them out loud. You can also try making up your own stories together.