Can I use the Verizon Iphone 5 in Europe just for internet?

I'm going on a trip for 2 weeks… Specifically London, Paris, Brussels and Amsterdam. I have a verizon iphone 5 and need it for internet access to make the trip smoother, but I do NOT need it for making phone calls or texting.
Do I even need a SIM card to use the internet in the various countries, or could I just use the free Wi-Fi at different places (which is what I want to do)?
Should I just call up Verizon to let them know I'm going to Europe but don't need any sort of phone package? I just don't want a massive bill of like $2, 000 when I get home!

You can use your iPhone everywhere in Europe just for internet. Just turn your Wi-Fi on and of you go. I recommend you turn your mobile data off so that you don't data roam while over there. Data roaming is very expensive so don't use it while traveling in Europe.