So what exactly do I need to turn off internationally to avoid some gigantic charge from Verizon?

MG2

 

On the AT&T phones you need to go into Settings, General, Network, and make sure Data Roaming is turned to off. Also, make sure Enable 3G is turned on on the same page as Data Roaming if you are in Japan or South Korea. They only have 3G and 4G networks available, so texting and the phone (for important or emergency calls only) won't work if 3G isn't enabled.
I would imagine the Verizon phones should be very similar.
One tip for finding restaurants or shopping using the Map functions while you are on an international layover. If you have an Airport Express to create your own network in your room, or you can go to a McDonald's or Starbucks to get on their network, you can zoom into the area you are in on the Map, find where you want to go, and move the map around the area a little bit. Once you leave the wireless network you're on, the map will keep that local area blow-up on the phone, and the GPS blue dot should be fairly accurate.
This also works in remote areas of the US outside of cellular network coverage.

 

Another option is to put your phone in airplane mode when overseas. You can then go back and turn on your wifi. No roaming.

 

I'm thinking this setup would probably get Internet functions only (weather, maps, Internet, email, etc.) but probably not phone calls if you wanted the family to be able to get in touch in an emergency. Turning off the data only (easier on some phone than others) would still allow you to receive emergency calls.

Can you can get texts via wifi?

 

Yes, maybe. The only change is now with iOS5, you don't actually use your messaging service for text messages iPhone to iPhone. You may have noticed that when you message another iPhone the message from you shows up as light blue vice the green when you message another "non" iPhone.

iMessage still uses your carriers data service, but it does work over WiFi. I just tried putting my iPhone in Airplane mode, with WiFi on and was able text my wife's iPhone no problem. I couldn't text my son, who doesn't have an iPhone. (ie the "blue" vs the "green" text bubble thing.)

 

You can text via email using (phone number)@txt.att.net which can get a message to someone who would normally not be checking email very often.

 

If you use mapswithme app you can download the whole city at once and access it later with the gps dot. Includes points of interest, not sure about restaurants.

 

viber : make high quality phone calls when you are outside usa. It's not as 'heavy' as skype.. Love it so far

 

You can get "Text Free" and it will allow you to text any cellphone just using a wifi connection. It also has a VOIP feature, but I don't use it.

 

These are the main apps I use:

WORK RELATED

PilotsGuide (Airport, weather etc)
FlightWare (Flight tracking)
AeroWeather (Precise weather forecast)
FlybyNav (Flight planning)
Viber (WiFi calls and texts - although the person on the other end must have this app as well)
Gorilla Expense (our expense management application for aviation departments)
Wi-Fi Finder (finds nearby Wi-Fi locations)

FUN

SoundHound (Recognizes any song, music etc and gives you the name)
WeatherChannel
Paper Toss (addictive game)
SkyView (constellations, space etc)

I am finding that using too many apps actually lowers my efficiency.