After a short introduction presenting Grenoble High Magnetic Field Laboratory and its high-field NMR facility, we will illustrate possibilities of high-field NMR in Solid State Physics on several examples of low-dimensional, quantum, antiferromagnetic spin systems. We further focus on two types of 2D, dimer, spin systems, which give raise to very different ground states under an applied magnetic field. One example is the "Shastry-Sutherland" compound SrCu2(BO3)2, which exhibits magnetization plateaus at fractional values of the saturation magnetization. In this compound plateaus appear because the kinetic energy of the triplet excitations is strongly reduced by frustration, so that the triplets can crystallize into a commensurate super-lattice. NMR signature of such a super-lattice in the 1/8 magnetization plateau of SrCu2(BO3)2 is a unique observation of this type of magnetization plateau created by spontaneous breaking of translational symmetry [1]. We shall also discuss some new results on the magnetic ground states at fields above the 1/8 plateau (i.e. above 28.4 T), which seemed to be a candidate for a supersolid phase. Another type of 2D spin system is represented by the so-called "Han purple" compound, BaCuSi2O6, for which there is no magnetic frustration, and in which a (2D) Bose-Einstein condensation of triplet excitations occurs above 23.35 T. We shall present a microscopic picture of this complicated high field phase, in which NMR data reveal that the average boson density in the condensate is strongly modulated along the direction perpendicular to the 2D planes, with a density ratio for every second plane nA/nB