There are two kinds of phone "apps".
The iPhone (iPad, iPod) Native apps
... these are written especially for those phones,
are downloaded into the phone, usually approved by Apple. Sometimes free, sometimes pay.
I suppose the same thing applies to the Android phones. Apps programmed just for them.
... these are basically web pages, and interaction designed specifically
for small screens, cell phones, PDA's, iPods, iPhones ... the "apps" are web sites that
the user visits ... sized for their phone. An example of this is: http://m.flickr.com/
So, you'll be looking at online apps (that's my guess).
Now, you have some other choices ... an app like flickr mobile, that is pretty much
a CSS/XHTML type of layout, or a more interactive design using JQuery
or jQTouch: http://jqtouch.com/
Here's an example of the jQTouch type of interface: http://www.meseim.com/mobile
You should really view those examples using a mobile phone, or iPod (not your desktop PC).
Once you determine what you will use to construct your app, you'll be getting into
the Google Map V3 part of it. I would focus on everything except the Google Map
until you get it all layed out. THEN, you can get into the Google Map part.
Give me the location of your park (GPS coordinates or link to a Google Map), and I
can give you an example of how to use that on a web page. The rest of it ...
layout, graphics, content, etc.... you'll have to figure out while I experiment with
your park map.