A lot of people ask me what to put in their diaper bag. Most diaper bags are huge, so filling them with nothing but diapers and wipes seems excessive, and it would be. Unless you are going on a long road trip or your baby is sick or something, there should really only be a handful of diapers on hand in your diaper bag. All of that extra space is for other necessities.
So, obviously I keep diapers, water wipes, and Desitin stocked at all times, but then I also
keep things that make being out of the house with a baby a lot easier. Things
like snacks (crackers, almonds, cookies, granola bars, etc. -- things that keep well), a handful
of building blocks, a couple Little People, a coloring book and a few
crayons, those foam alphabet cut-out things, a musical toy, and some
flash cards. If we'll be out for a while, I'll also bring extra juice.
My little one is 2 years old now, so obviously some of what
is in there would be silly for a newborn. But basically you want things
that are age appropriate to snack on, drink, and play with to keep baby content while out and about in. Most public displays of unhappiness (aka tantrums) are the direct result of hunger, thirst, and boredom. I mean, think about it, how excited were you to sit in a shopping cart for 30+ minutes as a kid while your parent(s) mill about seemingly aimless? Probably not very.
It wouldn't be a bad idea to keep a min first aid kit stocked as well. A few bandaids, some neosporin, alcohol wipes and so forth. It's not as likely to see use the first year, but after that your toddler is going to, well, toddle. There will be a lot of bumps and scrapes. Sometimes even if the boo-boo doesn't need a bandaid, sticking one on makes them feel better.
would also strongly suggest an entire spare outfit! I cannot count the
times this has been a life saver for us. Whether it be a poop explosion,
spit-up, barfing due to car sickness, getting rained on, falling in
mud, etc. Having that spare change of clothes is worth the room they
take. To minimize bag-space the spare outfit I usually pack is pajamas
(because things like jeans and sweaters take a lot more room). Just so
they have something dry and warm to wear home. If it is cold out, I keep a pair of mitten and a hat in there too.
If you'll be out a while, or are perhaps headed to swim or play at a wading pool, you should also bring along your baby's sunscreen as it needs to be reapplied every few hours (and a lot more than that if you're getting wet).