You don't even really need to "hold the camera steady" so much anymore, since most point and shoots (including the Canon I listed above) have built in optical image stabillization. This means that you can shoot without blur at shutter speeds of as low as 1/5 sec, provided that your subject is not moving.
The problem with P&S viewfinders is that most of them are quite bad...none of them can hold a candle to a true DSLR viewfinder. If you want the viewfinder composing experience with something that's bigger and offers 100% frame coverage, you might want to look into a camera with an electronic viewfinder, which is essentially a small LCD mounted where the viewfinder should be. EVFs are quite usable on a day to day basis and certainly better than the small optical viewfinders on most point and shoots. Plus, an EVF has 100% frame coverage and displays additional shooting information much like a DSLR's viewfinder.
The Panasonic FZ28 is their newest EVF superzoom. Look into that if you really appreciate having a viewfinder. If you can get over not having one, then the Canon A590 IS and Panasonic LZ8/LZ10 are three very good choices. All cost between $100 and $150, which is quite a bit lower than your target price. The A590 IS has a 4x zoom with optical IS; both of the Panasonics have 5x zoom with optical IS; the zooms on the Panasonics go slightly wider than that on the Canon, which is helpful when you can't move very far back for a shot.