We took a 4 month old this past September and it was really nice-she sort of forced us to take it a bit more leisurely. I loved the baby centers and selfishly wish there was more than one in each park. It is not always realistic to run back to one just to feed her (I was breastfeeding). My DH & DD 3 would hang out and watch cartoons, browse in a nearby store or go on a nearby ride. I also BF her in dark shows like the Laugh Floor Comedy Club. Just sat in the back row and made sure I kept us as covered as possible.
Most anything you need you can buy at the baby centers (formula, pacifiers, bibs, medicine, diapers, etc...it just costs more than you wish it did.
We used both a stroller and a bjorn. The bjorn (or any carrier-I think a nice light weight sling would be great) is nice for while we are on rides or going into shows. When we we wearing her we didn't have to deal with getting her in & out of the stroller, especially important when baby is sleeping. Yet, the stroller was great for walking around and giving us a break from carrying her. (We did not bring the infant car seat/travel system type stroller. 3-4 months is a little young for most strollers, but umbrella stroller/hammock type seat worked well for us at 4 months old).
September was HOT and so we were very conscious of keeping her from getting overheated and keeping her hydrated.
We took a smallish sized back pack with just enough supplies. I really tried to keep the extras to a minimum. I fought the urge to pack an overabundance of diapers, I grabbed only a handful of wipes, one extra outfit. I figured if we really needed more of something we could buy them in the parks. A few ziploc baggies in larger sizes helped out-to keep wet or dirty clothes separate from other things in your bag.
She had a lot of fun, I think. She was smiley and we spoke with many people because of her (no one can resist a smiley baby). I think her fave was It's a Small World, but isn't it every little ones fave? All the audio & visual stimulation.
Have fun!