There are lots of options for computer access while traveling. The benefits are many, from EMail to travel help and assistance, including using the computer as a guide, even in a museum.
Simplest, course, is not to take along a computer at all, but to use computers along the way where available. Hotels without free computer use can be avoided in favor of those with a free available computer. Libraries enroute often have computers and access.
It is a help to have all your applications on Google, so that you can access personal EMail, phone and EMail list, bookmarks, calendar, itinerary, and so on , anywhere there is a computer. For that, set up a GMail account, and Google Calendar, Docs, etc. so that you can get to all phone numbers, addresses, and EMail anywhere.
The next simplest and most useful thing to do is take along a tiny $10 USB flash drive with such information on it, even along with applications like a browser. Use it, again, wherever a computer is available.
With a little more heft you could take along a smartphone with wireless and internet, such as an iPhone, or a cheap handheld equivalent without cell contract, such as an iPod Touch or Zune. Skype should be installed on the device. The iPhone is the most versatile of all cell phones, and also smallest, but there are new ones in the Palm Pre and MyTouch. The iPhone/iTouch are full computers and can record messages, read ebooks and audible books as you travel, even take notes. The latter device needs wireless for some functions.
Free wireless access is available in many hotels and even in airports such as St. Louis and Phoenix, via a few airlines on the plane, and in places like Panera's. Find out before your trip. Newly, there are pocketable "hotspot" devices, such as the Verizon MiFi, which give you internet anywhere at all, even out walking.
If you want something bigger, and especially, if you want to originate documents anywhere, you may want at least a netbook, preferably one with solid state hard drive, (nearly indestructible), and/or, with a USB drive or SD card for backup of documents, so as not to lose your travel notes.
These come for as little as $200, up to $400, and from 7" diag screen to 10", the latter having a comfortable keyboard. They are a target for theft, so keep one locked up or in the small pack you carry with you at all times. The smaller iTouch above fits into a tiny beltpack, of which there are excellent ones under $10 on Amazon.
You must show your netbook or laptop to airport security. You can put your computer into a very small case with charger cables, pills, and even overnight essentials, and check everything else weighty. Case Logic and Targus make bags which get rave ratings on Amazon.
A surprising number of travelers take along a larger MacBook laptop, often seen in airports and planes. Next most often seen is a smartphone or iTouch.
The cheapest way to have everything with you is to carry your internet device, smallest camera (preferably including video), and GPS. Instead of all three, a netbook, though, can handle Skype where there is WiFi, and even GPS. The last, GPS, is invaluable in traveling, even just to safely find the correct route and lane, nearest rest stop, gas, or, restaurant.
I travel light and take along a small Nokia device which already has camera, Skype, GPS, and satellite TV access, but I carry a tiny camera and gps, too, and I use hotel computers. I carry a cell phone. An iPhone alone would handle it all, even without wireless, all in one tiny device, which can also serve as an ebook or audible book reader wherever you are.