Hundreds of loci have been associated with blood pressure traits from many genome-wide association studies. We identified an enrichment of these loci in aorta and tibial artery expression quantitative trait loci in our previous work in ~100,000 Genetic Epidemiology Research on Aging (GERA) study participants. In the present study, we subsequently focused on determining putative regulatory regions for these and other tissues of relevance to blood pressure, to both fine-map these loci by pinpointing genes and variants of functional interest within them, and to identify any novel genes. We constructed maps of putative cis-regulatory elements using publicly available open chromatin data for the heart, aorta and tibial arteries, and multiple kidney cell types. Sequence variants within these regions may be evaluated quantitatively for their tissue- or cell-type-specific regulatory impact using deltaSVM functional scores, as described in our previous work. In order to identify genes of interest, we aggregate these variants in these putative cis-regulatory elements within 50Kb of the start or end of genes considered as "expressed" in these tissues or cell types using publicly available gene expression data, and use the deltaSVM scores as weights in the well-known group-wise sequence kernel association test (SKAT). We test for association with both blood pressure traits as well as expression within these tissues or cell types of interest, and identify several genes, including MTHFR, C10orf32, CSK, NOV, ULK4, SDCCAG8, SCAMP5, RPP25, HDGFRP3, VPS37B, and PPCDC. Although our study centers on blood pressure traits, we additionally examined two known genes, SCN5A and NOS1AP involved in the cardiac trait QT interval, in the Atherosclerosis Risk in Communities Study (ARIC), as a positive control, and observed an expected heart-specific effect. Thus, our method may be used to identify variants and genes for further functional testing using tissue- or cell-type-specific putative regulatory information.