I have seen a few users suggest using a mobile wifi device -- a portable wifi hotspot -- as one solution to the problem of getting phone and data coverage in a foreign country. (See, for example, the comments from Jane regarding hippocketwifi.com in cell phone service .) This suggestion may bypass and solve a number of issues with keeping connected while traveling.
First, you can keep your current phone and number, assuming that your carrier supports wifi calling and texting. Just set your phone to airplane mode and then turn on wifi and connect to the hotspot. Calls to and from your phone that are to or from U.S. numbers should cost nothing additional.
Second, calls to an international number may be charged at expensive rates unless you use one of the much cheaper services that send calls over a data connection (Skype, Google Voice, etc.) But you can do that because you are using only wifi.
Third, carrying your own wifi connection with you lets you forget about trying to locate someone else's wifi, and skip worrying about whether that wifi will be adequate for you to use. (No more going to a McDonald's for the wifi.) If you are using your phone for directions, you can get directions on the move because you are carrying the wifi with you.
Fourth, most of the services I have seen will ship a wifi hotspot to you or you can even pick a device up at an airport or your hotel on your arrival. To return it, you usually mail it back in an envelope the company provides.
Fifth, the device should have the correct telephone radio frequencies to work where you are traveling. It is possible that your phone may not have everything you might need to get the best reception.
Sixth, the connections the device provides can be shared among several people so those traveling together might need only one device.
Seventh, the data limits on these devices may be greater than what your cell phone company allows and it may be at a faster speed.
Eighth, the approach is simpler than many of the other ideas.
I have not personally tried this solution yet, but I have considered it for all of these reasons. I would be curious to hear the experiences of others who have taken this approach. Did it work for you?