ATT doesn't sell wifi, however they do sell their own 3G data services. For a PDA phone, it's typically a $30 per month feature added on top of the voice plan. If you can do a *handset only* upgrade through ATT like I did online via ATT's online account manager (OLAM), perhaps you could acquire a wifi enabled handset that does not require an additional 3G data plan ($$). Normally their new contract phone discounts require such data plans.
In any case, sticking to wifi means you choose the locations where you connect to the internet via wifi. ATT does not monitor or charge for this feature. Some public libraries offer wifi it for free; other places like Starbucks might charge a fee, it depends where you are trying to use it. ATT doesn't charge because you aren't getting your data via their 3G network.
On my phone I use a program to turn off access to ATT's 3G data network so I don't accidentally get charged a la pay per use. When I want to access data via wifi, I push a button to turn on the wifi radio, enter a password if necessary ,etc. At home I have it configured to automatically connect to my home wifi when it's in range. At work it requires a password so a box pops up when I'm in range of the access points throughout the buildings.
Regarding unlocked phones, a handset is unlocked when another carrier's SIM card may be used to obtain service. In other words, when you travel you could obtain a foreign pre-paid SIM to avoid the high international roaming charges from a U.S. carrier. In the U.S. you could use an unlocked ATT branded handset with T-Mobile if you wanted to use their service. Voice is never a problem in this regard, but 3G data can be now since T-Mobile uses slightly different frequency bands on their handsets for 3G data. In this sense, an ATT smartphone might not function completely on T-Mo's 3G data network since it lacks the correct bands.
Hope that helps a little more.