We present NuSTAR hard X-ray observations of Sh 2-104, a compact H ii region containing several young massive stellar clusters (YMSCs). We have detected distinct hard X-ray sources coincident with localized VERITAS TeV emission recently resolved from the giant gamma-ray complex MGRO J2019+37 in the Cygnus region. Fainter, diffuse X-rays coincident with the eastern YMSC in Sh2-104 likely result from the colliding winds of a component star. Just outside the radio shell of Sh 2-104 lies 3XMM J201744.7+365045 and a nearby nebula, NuSTAR J201744.3+364812, whose properties are most consistent with extragalactic objects. The combined XMM-Newton and NuSTAR spectrum of 3XMM J201744.7+365045 is well-fit to an absorbed power-law model with ${N}_{{\rm{H}}}=(3.1\pm 1.0)\times {10}^{22}$ cm−2 and a photon index ${\rm{\Gamma }}=2.1\pm 0.1$. Based on possible long-term flux variation and the lack of detected pulsations (≤43% modulation), this object is likely a background active galactic nucleus rather than a Galactic pulsar. The spectrum of the NuSTAR nebula shows evidence of an emission line at E = 5.6 keV, suggesting an optically obscured galaxy cluster at z = 0.19 ± 0.02 (d = 800 Mpc) and L X = 1.2 × 1044 erg s−1. Follow-up Chandra observations of Sh 2-104 will help identify the nature of the X-ray sources and their relation to MGRO J2019+37. We also show that the putative VERITAS excess south of Sh 2-104, is most likely associated with the newly discovered Fermi pulsar PSR J2017+3625 and not the H ii region.