The fix is simple: Turn Wi-Fi Off. If you leave Wi-Fi on it is going to try and find an open network to connect to.

A possible work around would be to get a program like JuiceDefender Plus/Pro, which will turn your WiFi on and off for you, depending on your location.

 

There is a setting that asks to tell you about open wifi networks.

 

Why do you not want to turn off wifi.? You don't want it to connect to wifi, so turn it off.

Honestly, simple answer.

 

Settings>Wifi>Click in the 3 dots in the bottom right hand corner>Advanced>avoid poor connections
That might help.

Or, now I'm too sure about this, turn off the wifi when not at home. 75% sure that someone has said that though.</sarcasm>

 

As far as I know, android will automatically connect only to known networks (networks you have previously told it to connect to). Are you saying your device is connecting to networks you've never connected to before? If so, do these networks have the same SSID as one or more of your known networks?

 

People don't want to turn off WiFi because it is a useful location tool which doesn't require GPS and therefore saves battery. If you forget to switch it back on when you get home the extra battery you'll use on 3G will far outweigh the minimal use it had whilst on in the background during the day, saving battery again. It's really an unnecessary extra step. I've tested this myself, and really found o advantage in turning it on and off all the time, and there are several advantages to just leaving it on.

Either of the solutions posted above will solve the OP's problem without just turning WiFi off...

 

I see 2 options here...
1) Turning of your Wi-Fi (which you clearly don't want to do)
2) Everytime your phone connects to networks you don't want to connect to, go to settings->wi-fi settings-> and then, click on the network you're connected to and click on it and then click on the "Forget" button. This way, your phone won't connect to those networks that are "forgotten"... Helps?

 

@Menddles - I don't have an "avoid poor connections" option there - are you on the stock ROM? (GSM? CDMA?)

@op On the Sprint GNex, there is a "network notification" checkbox in the advanced menu of wifi settings. (description is "Notify me when an open network is available")
If that is available on your VZW GNex, uncheck that - does that help?