Having occasionally been able to have a play with pianos and thinking I'd like to learn to play I've been trying to find the same thing. So far I'm looking at the Casio CT-S1. It's a 61 key piano focused keyboard (so while it doesn't have the weighted keys you'd find on an actual digital piano, it is a little closer to the feel of a piano than a typical keyboard) with great built in sounds and speakers plus midi over USB for use as a midi controller with your computer. They're designed specifically to be highly portable so they are light and have a relatively low footprint for a 61 key. I dunno about the US market but in the UK they're generally available around £200 so I expect it's likely to be about $200 over there. People also seem to rate the Yamaha E373 but from what I understand it has a more keyboardy key style (ie, rounded rather than flat ends, no texture and very little resistance) and it is a bit bulkier and more complex to use. The flip side is that you get way more sounds (though I gather that the high quality sound selection is similar between the two) and more direct control to edit and adjust those sounds. There's also the Roland GO:Piano, which is overall quite similar to the Casio CT-S1 but I hear the key-feel (whilst possibly more piano-like than the E373) isn't as good as the CT-S1.
Ultimately there just aren't any affordable non-88 key digital pianos. The big difference being the key action. The three keyboards above all offer great piano sound and dynamic playing (ie, the harder you press the louder it plays). It seems (having not had the chance to try any of them myself) like the CT-S1's key feel is the least un-like a piano's of the three.
The next step up would be something like the Roland FP-10 but that's nearly twice the price of these keyboards (and personally I'll have to save a looong time to be able to afford a £200 one so that's out until I'm seriously committed) and, while they are portable digital pianos, between the full 88 keys and all the extra bulk and mass of a proper weighted keybed they're still gigantic and heavy compared to some of these "piano"-style 61 key keyboards (not to mention that I hear you have to always keep digital pianos horizontal or you eventually damage the weighted key mechanism, whereas afaik a portable keyboard is more flexible in how you store it.)