Tip-enhanced Raman spectroscopy (TERS) has experienced tremendous progress over the last two decades. Despite detecting single molecules and achieving sub-nanometer spatial resolution, attaining high TERS sensitivity is still a challenging task due to low reproducibility of tip fabrication, especially regarding very sharp tip apices. Here, we present an approach for achieving strong TERS sensitivity via a systematic study of the near-field enhancement properties in the so-called gap-mode TERS configurations using the combination of finite element method (FEM) simulations and TERS experiments. In the simulation study, a gold tip apex is fixed at 80 nm of diameter, and the substrate consists of 20 nm high gold nanodiscs with diameter varying from 5 nm to 120 nm placed on a flat extended gold substrate. The local electric field distributions are computed in the spectral range from 500 nm to 800 nm with the tip placed both at the center and the edge of the gold nanostructure. The model is then compared with the typical gap-mode TERS configuration, in which a tip of varying diameter from 2 nm to 160 nm is placed in the proximity of a gold thin film. Our simulations show that the tip-nanodisc combined system provides much improved TERS sensitivity compared to the conventional gap-mode TERS configuration. We find that for the same tip diameter, the spatial resolution achieved in the tip-nanodisc model is much better than that observed in the conventional gap-mode TERS, which requires a very sharp metal tip to achieve the same spatial resolution on an extended metal substrate. Finally, TERS experiments are conducted on gold nanodisc arrays using home-built gold tips to validate our simulation results. Our simulations provide a guide for designing and realization of both high-spatial resolution and strong TERS intensity in future TERS experiments.