Tissue stiffness is related to soft tissue pathologies and can be assessed through palpation or via clinical imaging systems, e.g., ultrasound or magnetic resonance imaging. Typically, the image based approaches are not suitable during interventions, particularly for minimally invasive surgery. To this end, we present a miniaturized fiber scanning endoscope for fast and localized elastography. Moreover, we propose a deep learning based signal processing pipeline to account for the intricate data and the need for real-time estimates. Our elasticity estimation approach is based on imaging complex and diffuse wave fields that encompass multiple wave frequencies and propagate in various directions. We optimize the probe design to enable different scan patterns. To maximize temporal sampling while maintaining three-dimensional information we define a scan pattern in a conical shape with a temporal frequency of 5.05 kHz. To efficiently process the image sequences of complex wave fields we consider a spatio-temporal deep learning network. We train the network in an end-to-end fashion on measurements from phantoms representing multiple elasticities. The network is used to obtain localized and robust elasticity estimates, allowing to create elasticity maps in real-time. For 2D scanning, our approach results in a mean absolute error of 6.31+-5.76 kPa compared to 11.33+-12.78 kPa for conventional phase tracking. For scanning without estimating the wave direction, the novel 3D method reduces the error to 4.48+-3.63 kPa compared to 19.75+-21.82 kPa for the conventional 2D method. Finally, we demonstrate feasibility of elasticity estimates in ex-vivo porcine tissue.