Be careful when simply wrapping things into a mobile app. This can backfire on you and you could be presented with some very harsh edge cases. PHP isn't going to be encapsulated so much as the HTML/CSS/JavaScript. So keep in mind your mobile application could likely be in a position of requiring an online connection to work (because it must interface with your existing hosted WordPress site). This could also mean your hosting solution needs to be evaluated to ensure you can handle any increased traffic (and those traffic patterns could be different when coming from a mobile app that perhaps loads things the user doesn't see right away, accesses content that may not be cached, etc.). You want to ensure your server doesn't go down because then your mobile app would be "down" as well.

That said... Things like Phonegap (web views) are a wonderful idea for utility apps because the performance is good enough for those (and hey even some games) and they end up being easily ported across many mobile operating systems.

I would look into Phonegap, Appgyver (a new and totally awesome one because parts of it will utilize the native OS and your app will feel more responsive), Appcelerator Titanium, and perhaps even the new Famo.us one. Also take a look at the Ionic Framework for some further ideas about mobile UI and what you can do with these web view style apps.