Urban monitoring using remote sensing is the most reliable and cost-effective method that provides high accuracy and multi-temporal data for studying urban expansion in horizontal and vertical dimensions. Vertical monitoring of urban areas includes mapping compactness, population growth, and study of urban surface geometry which plays an essential role in the applications of urban heat islands, generation of urban canopy layer, etc. The presented study uses the Ice, cloud, and land elevation satellite-2 (ICESat-2) ATL 03 photon data for building height estimation for a sample of 30 buildings in three experimental sites. The heights computed from the ICESat-2 profile were compared with google images of respective buildings for the accuracy assessment. The results when compared to the ICESat-2 reference data give an RMSE of 2.04 m. Another popular way to map the vertical dimension of terrain in urban areas, that are globally used by policymakers for resource management, planning, and maintenance is the Digital Elevation Model (DEM). It can be generated using various remote sensing techniques but the usage of active remote sensing procedures has an advantage over passive methods due to their capability to function both day and night irrespective of weather. Thus, the study further aims to assess the openly accessible DEM products available from TanDEM-X, which is a German Earth observation satellite that uses InSAR (Synthetic Aperture Radar Interferometry) technique, and Cartosat-1, an optical stereo acquisition satellite launched by the Indian Space Research Organization (ISRO). Taking ICESat-2 (ATL-08) Elevation data as reference, the accuracy of two study sites was checked by statistical measures such as Mean error (ME), Mean absolute error (MAE), Root mean square error (RMSE). In the urban area of Greater Hyderabad Municipal Corporation (GHMC), an RMSE of 5.29m and 7.48m were observed for TanDEM-X 90 and CartoDEM V3 R1 respectively, while the same showed an RMSE of 5.15 and 5.48 in the Bellampalli Mandal rural site respectively. The DEMs exhibited better results for the Bellampalli Mandal rural area of Telangana State as the built-up is sparse and the terrain is mostly flat as compared to the GHMC site. The results show that the accuracy of TanDEM-X is better as compared to the CartoDEM V3 R1. These results can assist the decision-makers and planners in choosing suitable DEMs for planning and management purposes for smart cities as well as rural settlements.