This would be my first option, too, although if the router and the computer are at opposite ends of the house it could be a problem. Then again, if the router and the computer are a long way away from one another, you might also have problems with your wireless connection.
I was facing this same problem with my intenet-connected TV and Blu-Ray player. Both of them come with wireless, but they are downstairs and at the opposite end of the house from my upstairs wireless router. The house isn’t that big, but i was still having trouble with the wireless, especially on the Blu-Ray player, with dropouts and slow connections.
I solved my problem with a powerline adapter kit. Basically, it allows you to use the electrical wires in your house to run a wired network connection from one part of the house to another. You plug one device into an outlet near your router, and one into an outlet near your computer (or, in my case, TV/Blu-Ray), and then run short ethernet cables from each adapter to the equipment. It works a treat, and avoids the hassles of wireless, as well as the hassle and unsightliness of trailing a long ethernet cable from one end of the house to the other.
I got my kit on special for about $40. It’s only a 200Mbps kit, but that’s plenty for my needs. The only reason to want a faster connection is if you’re using the link to transfer lots of files from one computer to another over your home network. For that sort of thing, 200Mbps can be painfully slow. I just use it to stream stuff from the internet (Netflix, MLB, etc.), and also to stream movie files from my computer. 200Mbps is more than enough for that; even a 10GB hi-def movie file doesn’t transfer at more than about 12Mbps.
One issue with powerline adapaters is that, according to some reviews, their effectiveness can vary from one house to another, depending on how new or old your wiring is, and how your electricity wires are configured. We’re in a pretty new place (<10 years old), and we’ve had no troubles.