I’m looking for a good flowcharting/mind mapping program that will allow me to work on my iPad, but also work from my Mac when I am home.
Lucidchart has a very robust mind mapping library.
I use Novamind. It has a 30 day trial and it isn't cheap but after trying all of the free options, it seemed to be the easiest one to use.
What exactly are you hoping for in terms of mind-mapping? I've looked into this subject extensively and there are a lot of options, both freeware and not-so-free-ware. Unfortunately, depending on what you have in mind, the availablity of iOS versions of the software varies a lot.
If you are looking for a simple way to brainstorm, choices like Mindnode, Freemind, and others on this page are great ideas. Personally, I think Freemind is still a bit clunky visually, and the other options are much more streamlined and easy. Also Freemind doesn't have an iPad version as far as I know. I have used Mindjet before, but (as with a lot of these apps) customizing the appearance and layout of the diagram is sometimes lacking--or perhaps requires an official subscription or more patience than I supply. If you don't care how the nodes are laid out or what they look like (for example, having it be connected bubbles instead of looking like branches of a tree), this shouldn't be an issue.
However, if you are looking for a mind-mapping software that is more along the flowchart/diagram like (more like a concept chart), and visual output is of concern, options like Cmaptools, Lovely Charts, and Omnigraffle might be of interest. I personally like Cmaptools for how flexible it is to maximize usable space in complex charts. However, it does not have an iOS app, while Lovely Charts does...however, the Lovely Charts iPad app gets lousy ratings (https://itunes.apple.com/app/lovely-charts/id485253769?ls=1&mt=8). Luckily, there are plenty of sites like Lovely Charts (such as Mindmeister, Mindjet, Mindomo, and more) that also have companion apps.
I've also heard interesting things about Oovium, which is a more sandbox-type/brainstorm-on-steroids. It has both Mac and iOS versions.
Mindnode, for sure!
For mindmapping, I'm very impressed by "Simple Mind".
Use Mindnode http://mindnode.com