We took the Eastern Europe land trip in 2011 with a netbook, used for eMail, Skype, and backing up pictures. In general, you will find wireless access to the Internet throughout the tour, but in some instances, you may need to look for it.
Hotels may have changed since our trip but I don't recall any problems with access in Berlin (Ramada Plaza City Centre), Warsaw (Radisson Blu), and Krakow (Radisson Blu). In Budapest (Courtyard By Marriott), I recall a rather steep charge but the McDonald's across the street or the shopping center next door provided free access.
The worst access was at the hotel in Prague (Dorint Hotel Don Giovanni). The charge for use in our room was unreasonable. They had two computers off the lobby, in what once might have been phone booths, that could be used at no charge but they were terribly slow. Those of us with netbooks/laptops found that by disconnecting the Ethernet cable from these and plugging it into our devices worked well and speed was acceptable. There also is a shopping center within walking distance where wireless access was free.
There is an advantage to bringing your own device in that keyboards differ in these countries. We used an Internet cafe in Prague for access to a printer to print our boarding passes. We had to ask for assistance to find certain characters (the @ sign I believe was one), and some keys are placed differently than the US keyboard. You also need to know how to switch Windows to display in English rather than the language of the country you are in.
All things considered, I would suggest taking your own laptop.