Ideas for what to do with an infant
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Go for walks. Go to the park. Go to the mall. Coffee dates (even if just you and kiddo). Infant classes like gymbaroo or baby sensory. Swimming. You get some mum friendly exercise classes that include childcare or incorporate your kid.
Ditto to the above and just to add - my second baby is 2 months old and this time around I got a ring sling so I’ve been wearing baby when I’m out and about. She LOVES to be snuggled near me and usually just ends up napping while I get to take my time walking around target, the mall, sip on a coffee, etc… I just make sure she’s well fed and with a fresh diaper before we leave the house.
Library, park, swimming, restaurants, museums, classes (baby gymnastics, dance, etc)
Go to the park, museum, gardens, zoo, coffee shop, mom groups, baby massage class, baby music class. It's more for a change of scenery and to get some air, but it's something. You could always invite a friend to tag along with you guys.
We go to classes, run errands, see friends, go to the zoo. Read and play at home, walk the dog.