Hmmm I haven't tried it, may go to Borders or Barnes & Nobles tomorrow just to try since I will be going on vacation this week and will most likely be connecting to the wifi in the hotel.
I tried my first iPad at Borders a long time ago, before I put any private info on it (haven't used public wi-fi since). It picked up Borders' wi-fi without problem.
I've used my iPad at a lot of free spots, with no troubles. Sometimes, you may be showing that you have a WiFi signal, but then you have to go into Safari and agree to the WiFi hotspot's provider's service agreement.
If you just go to the hot spot to check mail, you may miss this part...
So, what is happening on your iPad when you try to use Border's hot spot?