My understanding is that you either want to learn how to analyze NMR data or test a new experiment on a well-behaving sample.
If you are interested in small-medium sized proteins in liquid phase then I recommend human ubiquitin. It is a very stable well-folded protein with five beta strands and two helical motifs. Beta strands and helices have different NOE patterns, so you can learn how to recognize those using the ubiquitin sample.
There is a lot of data published on ubiquitin, including Biomolecular NMR Data Bank - BMRB.
Also there is a ubiquitin NMR resource website built by Richard Harris at the University College of London that has 17 2D and 3D data sets together with nmrPipe processing scripts.