Just check with your pediatrician re:sunscreen. What mine had told me was that they didn't want you to use it on under 6 month old, because they didn't want babies that young in the sun too much. That being said, he said it was better to use it if you have to be in the sun.
My daughter was under 6 months old my first summer with her. I had a great canopy on the stroller, a hat on her head, sun glasses and one of those sun blockers that you attach to the stroller, looked for shady spots when I needed to take her out of the stroller.
I took my daughter to Disney at 11 months old and I can attest to how great the baby centers were. I think they even gave away diapers at one of them (the other might of sold them). Plus, they had formula, baby food, etc. And while some people might be bothered paying Disney prices for this stuff - it was great not to have to lug it around all day. Plus, they had air conditioning, rocking chairs galore for feeding and were just the most comfortable place to relax in the parks outside of a hotel room.