Here is the proton nmr spectrum for pyridine.
Here is the proton nmr spectrum for furan
For comparison, benzene has a single proton nmr signal at 7.27 ppm. In both pyridine and furan there are different types of protons, so multiple signals are seen in both cases.
Here are the resonance structures for pyridine
Pyridine removes electron density from the alpha and gamma positions by resonance while furan adds electron density to all four ring positions by resonance.
In addition to resonance effects there are also inductive effects and ring currents that will modify the proton chemical shifts. Inductively, the alpha positions in both molecules will be deshielded. Ring currents will also deshield the protons as you've noted.
All of the signals are in the general vicinity of benzene. The alpha-protons in both molecules are the most deshielded due to inductive effects, with furan's alpha signal upfield from pyridine's due to the electron donating resonance effect of the furan oxygen. The beta proton in furan is the most shielded since it is not inductively deshielded and, again, the oxygen in furan is pushing electron density into the ring via resonance which will cause shielding.