I've noticed that the GTab 10.1 does not like adhoc wifi networks and certain wifi WPA/WEP encryption.
I'm assuming the public places where it connects have open, unsecure connections? Does it connect when your router is unsecure?
I am delighted to assist you with our wifi on your Samsung Galaxy. Are we talking about a tablet or a phone? May I ask that you specify the model of the device we are assisting with? i.e. Galaxy Tab 10.1, Samsung Fascinate, etc. Are you able to connect the Galaxy and the iPhone to your home wifi with the password disabled? IF you haven't attempted this step yet then I would encourage you to try. Finally, what wireless security setting are you using, WPA or WEP? I'm looking forward to your reply so I can provide additional assistance.
Change the router broadcast channel, my guess would since you are experiencing it on multiple devices you may be getting interference from a neighbors wi-fi that is broadcasting on that same channel.
If you are on a Mac download a free application called iStumbler, I'm not sure what the Windows equivalent would be.
I've had my Gal Tab (7", SCH-I800, v2.3.5) since May and have had the same WiFi no-connect problem. In searching a lot of blogs for others having the same problem, it seems the issue is with, for one, Belkin routers - the Tab will not connect to at least some models of it. I was sad to discover that because, of course, I have a pretty new Belkin at home and am not replacing it. A workaround was to tether onto my home's WiFi through my Samsung laptop Windows 7 home networking ability. It nicely provided a 'tunnel', if you will, to the internet for my Tab. But, low, after the last firmware upgrade on the table to 2.3.5, I am no longer able to connect via Win7 : (
Hopefully, some of that is useful info.