There are tons of little solid-state amps that have headphone outs and will give you a good sound. (The Roland MicroCube, for example, is a very popular choice

There are tons of little solid-state amps that have headphone outs and will give you a good sound. (The Roland MicroCube, for example, is a very popular choice. I even have one, and I'm normally a boutique tube amp snob.) There are also little battery-powered headphone amps that clip onto your belt, but they tend to really suck sound-wise. Something like a MicroCube would be a better investment if you think you'll stick with it for any length of time.