Welcome to PF
there are just so many questions in physics remained unanswered! interesting ones? that's depends on your perspective and taste. Some examples (choose you own favorites):
quantum computing/information (theory, algothrim development, fault tolerant, error-correction, encryption, measurement, entanglement...)
quantum computing/information (material science: silicon, diamond for solid state QC, spin-readouts, single-electron transistors, quantum optical system...)
observational astronomy/astrophysics/cosmology (quasars evolutions, pulsars EM fields, pulsars Gravitational waves, LIGO, reionisation epoch, drawf galaxies, gravitational lensing, gamma ray burst, dark matter halo...)
Experimental particle physics (LHC, ATLAS, Belle labs: search for supersymmetric particles, Higgs bosons, extra-dimensions, 5D black holes, neutrino mixing angles, CKM matrix parameters, dark matter candidates, collider technologies, sychrotron technologies, grid computing, B physics, CP violation)
Theoretical particle physics (strings theory, branesworlds, grand unified theories, flavor symmetries, supersymmetry, supergravity, quantum loop gravity, lattice gauge theory, QCD, unparticle physics/scale invariant models, , B physics, CP violation, dark matter annihilation, mini-black holes, topological defects, early universe: Baryo/leptogenesis, inflation, quantum gravity, dark energy...)
condensed matter (superconductivity, phase imaging/inverse scattering problem, nonlocality in scattering, microanalysis, Bose-Einstein condensates, breakdown of the integer quantum Hall effect, many body problem, electron microscopy, disordered systems, statistical mechanics, ...)
quantum/classical optics (phase microscopy, X-ray optics, atom optics, ultracold plasma, laser interferometry, instrumentation and technology, optical fibres, precision test of QED, synchrotron beamline developments, X-ray crystallography, ...)
also nuclear physics, other material physics, mathematical physics, plasma physics, nuclear fusion... this's just a small sample (biased by what I and what ppl around me here do)... the list is endless ...
