Single Dad here.
I have traveled to the parks 3 times with just me and my kids. Once with a 2 and 3 year old girls, once with 4 and 5 year old girls, and once with 7 and 8 year old girls. It is always magical, but sometimes difficult with only one adult. (especially when I need to use the bathroom).
Based on your child's age, here is some advice:
1. Have a good stroller. A jogger stroller is preferable because of the ability to carry so much extra stuff.
2. Have extra drinks and snacks with you at all times. Getting food is a lot more difficult and time consuming with only one adult. Having a quick granola bar or fruit snacks to tide them over makes things a lot easier.
3. Spend some time at the various playgrounds in the parks. It is a great time to let them run off steam while you can sit and catch your breath.
4. Bring a blanket with you and plan on taking lots of naps. I found when I put my tired kids in the stroller with a blanket and rolled around the parks, they fell asleep in no time.
5. Plan for extra time. Getting on and off the buses, getting stuff from the stroller, or general navigation is sometimes more time consuming without two sets of adult hands. You have to watch your kid and do something at the same time, in a busy crowd. It will take longer, so plan for it.
6. When in doubt, ask a Cast member. They are great for helping distract your kid while you do something. (like go to the bathroom)
Good luck! It is always fun. And just think of how lucky you are to be the only one who sees the Magic in their eyes when you take them to the parks!