Don't forget to use your personal copy of Organic Chemistry Online; the path you want is [CD Drive letter]:\OCOL_HTM\OCOL\OCOL.HTM. The lecture slides for NMR may be downloaded here.
nmrdb.org will either find or calculate a 400-MHz 1H spectrum for almost any compound.
WebSpectra is probably the best public spectroscopy drill site on the web. It includes some tutorial material. Most problems are NMR only, but some include IR. All problems give the molecular formula.
The Organic Structure Elucidation Workbook now includes problems at all levels of difficulty. All problems include a mass spectrum, but spoil it by also giving you a molecular formula! They also don't supply a solution...
John L. Nash's 1H NMR Spectra of Small Molecules is useful in that it allows you to see correlations between spectral and structural features. An associate site shows vibrational modes of selected small molecules. These pages require the Chime plug-in.
Joseph Hornack's online textbook The Basics of NMR is pretty comprehensive. He also has a textbook on MRI that duplicates some of the material, and is pretty interesting.