Laptops can be handy, but they're a pain to carry around. If you get one with a larger (over 15") screen, the weight tends to add up fast! One alternative is to carry a low-powered device that will let you check your email (and Facebook!) and maybe do some simple word processing, but without all the features - and weight - of a full computer.
You have a couple of options here. One is a netbook; these are small, low-power computers that are mostly designed for web surfing rather than doing serious processing. If you keep everything on the web (using Google Docs, for example, rather than Microsoft Office) this might actually be all you need, and you can pick one up for under $300. One issue that I've had with netbooks is that, due to their small size, they can be a bit of a pain to type on; also, they generally don't have optical drives, so you can only get files on and off of them by using the USB port (plugging in either a USB drive or an external optical drive) or over the network.
Another option, of course, is to get a tablet. Chances are, when I say tablet, you hear iPad. Which is fine; while there are a number of different tablet computers available, the iPad is probably the most user-friendly, and it certainly has the most available applications! People who prefer to have more control over their computing experience might prefer an Android tablet. Either way, these are essentially large netbooks adapted to use touchscreens rather than other forms of input (although you can generally hook up an external keyboard if you prefer). Tablets have the same advantages as netbooks, as well as additional applications made specifically for them (Apple's app store, for example); the trade-off is that they tend to be a little more expensive.