What image size do I need to print a 4'x4' photograph?

There isn't really a minimum resolution, it's more a case of keeping the pixels small enough that at your expected viewing distance they're not individually visible. If by "hung in a stairwell" you mean on the wall at eye height that people will pass within a foot of, then that's pretty much worst case scenario - extreme close range viewing distance of a large print - and you'll want either a high res image, or to make a decent interpolation. At that (closely examined) distance, thanks to the canvas texture, I'd think you could get away with 50 pixels per inch (ie an image about 2500x2500) if it's high quality (ie not riddled with jpeg artefacts, which will show up pretty nastily at that kind of resolution. Not a lot of pixel noise or hard transitions). If you don't know a lot about your camera settings, chances are that your images will have a bit too much noise and artefacts at this kind of res. A safer option would be for an image of 3000x3000 or higher, and interpolate it up to 5000x5000 (which smears the pixels out a bit, making them slightly less intrusive) or if you can get at non-interpolated image at that resolution, go for it! (but it's actually pretty unlikely to be uninterpreted) Basically, take a look at some of your photos zoomed right in, so you can see the pixels. If you can now see all sorts of artefacts and noise, you'll want to clean it in photoshop before printing (hell, do that regardless). If there is a lot, it might not be easy to get nice results. Also remember, you could cut one sixteenth of your photo out, and print it on canvas at 1x1 foot as a cheap test-print, and see how it comes out. That will be very informative, and that knowledge will make you feel much more secure about ordering the 4x4!

Since the technical questions are answered... Try Costco.com or go to the store. You don't have to be a member to get your pictures printed. Just go to the customer service desk or some Costco stores have a photo section right next to the customer service desk. Also check out Groupon. I get e-mail notifications regularly for canvas prints that are very affordable.

as far as finding images, check out http://sxc.hu for free stock art

If you can plan the photo and shoot something specifically for this rather than using something you already have, you could do a composite photo and stitch it together using tools in Photoshop or little open source utilities. (Not really an option for stuff that moves of course, but I've seen amazing results for landscape type stuff.) It takes a little practice but it's not that tough if you have a tripod and any kind of software to help, and even with an 8mp camera, a composite image made of 2x2 or 3x3 images would give you a lot of resolution to work with compared to almost any single shot. A grid of 4 shots by 4 shots stitched into a 4' x 4' picture could have stunning detail even at that output size.

Contrary to what Yellow said above, you DO need to have a Costco membership for photo work. (Exceptions are food court and pharmacy.)

This http://www.have-camera-will-travel.com/field_reports/the_300_dpi_print_myth.html discusses what really happens at different DPI. I like perfectposters.com. Even if you don't use them, they have a great series of http://www2.perfectposters.com/aptarticles2.htm on image size, paper type, etc.

W/r/t resolution, I would really, really get the recommendation of the vendor you choose. Why? Well, many dpi calculations are based on half-tone screening; that is, breaking the different lightness and darkness values (of each ink, cmyk, for color) into a little dot that occupies a percentage of a cell in a matrix that makes up your picture. So when you start to have fewer pixels in than you have cells going out, you start to see square edges. However, what with all the newfangled digital doodley-dads, images can be more easily screened http://www.printsourceinfo.com/StochasticScreening.html; instead of a grid matrix, the values are "pseudo-randomized"! And "frequency modulated"! I have seen it work wonders for images whose input size were severely inadequate by halftone standards. So the vendor themselves should have the best way for you to balance resolution vs. file size based on their postscript methods.