Location based social networks (LBSNs) are becoming increasingly popular with the fast deployment of broadband mobile networks and the growing prevalence of versatile mobile devices. This success has attracted great interest in studying and measuring the characteristics of LBSNs. However, it is often prohibitive, and sometimes impossible, to obtain a detailed and complete snapshot of a LBSN due to its usually massive scale and the lack of proper tools. In this work, we focus on sampling and estimating restricted geographic regions in LBSNs, such as cities or states, in Foursquare. By utilizing the geographic search APIs provided by Foursquare, we propose a random region sampling algorithm that allows us to draw representative samples of venues (i.e., places), and design unbiased estimators of regional characteristics of venues. Moreover, using a unique dataset with 2.4 million venues, that we collected from Foursquare, we further explore the factors affecting the venue popularity, and present our preliminary findings, with applications in venue recommendation and advertising in LBSNs.