Jenny Guay of the blog Furiously Eclectic, has a fun knitted dishcloth pattern called the Five Stitch Dishcloth. It's a free pattern, and a fun one. Her pattern is based on the Ten Stitch Blanket by Frankie Brown, which uses the same construction concept, just on a larger scale.
The basic idea is that you knit a small square and then proceed in a coil around that square until the piece reaches the desired size. The corners are made using short rows, and each new coil is attached to the work as you go, at the end of every other row. For a knitter who is confident in their basic skills, this is a fun and easy project that neither requires too much thinking nor gets boring. It's also nice to make something bigger where there are no seams at the end, but that also allows you to work all the stitches on a pair of glove needles if you want to. While this project is a good introduction to short rows, the small number of stitches make the project a little fiddly, so I would not recommend it for a truly beginning knitter. For the less experienced, the Ten Stitch Blanket might actually be a more manageable option.
I haven't tried Brown's Ten Stitch Blanket, but the Five Stitch Dishcloth is well written and easy to follow. Still, in making a couple of these dishcloths, I tweaked the pattern a little to create an appearance I find more appealing. One side of the dishcloth (the "right side") is very smooth, and the built-in seams are barely visible. The other side ("wrong side") has a raised seam where new rows are joined to the already worked coil. Following the pattern as written, I thought the wrong side seam looked a little sloppy, and I wasn't happy with it. Tweaking the pattern just a little, however, created a seam that looks almost like i-cord appliqued to the surface. This variation is more visually apparent than the seam is in the original instructions, but it creates a strong, outline of the square coil that I like. The right side looks about the same whether using the original instructions or this variation.
The original pattern proceeds like this between the short-rowed corners:
"Row 1: slip 1 [purlwise, wyf], k3, slip 1, pick up and knit a stitch from the side of the row, pass the slipped stitch over (You should still have 5 stitches)
Row 2: k5"
Instead I did this:
Row 1 (RS): slip 1 purlwise wyf, k3, slip 1 purlwise wyb, pick up and knit a stitch from the side of the row, pass the slipped over (You should still have 5 stitches)Row 2 (WS): slip 1 purlwise wyf, k4.
It's a really simple change that, I think, significantly improves the visual impact of this technique.