I was recently stuck on a Chromebook which is pretty much a laptop built around a browser. This meant no Inkscape or Adobe Illustrator for me! I found a fork of Googles SVG edit called MethodDraw:
http://editor.method.ac/
It lacks a working grid in the current alpha, but just about everything else is there for making quick sprites.
I really prefer the layout to Inkscape for quick doodles.
It exports .PNG and you can save in a very clean SVG format as well. It is very easy to read in a text editor if you decide to animate it later. (Great for webpage logo's and headers. SVG loads very fast!)
It is just HTML5 and JavaScript so you can probably run it with a tablet too.