Accessing Expression Levels for Genes of Interest from GEO Experiments
You could look at supplementary and methods section of "The Landscape of Long Noncoding RNAs in the Human Transcriptome" paper. They've collected RNASeq samples from TCGA, ENCODE and MCTP and processed it with their pipeline (most of it are filtering and GSEA) to detect novel lncRNAs and associate them with cancer pathogenesis. Their statistics, processing and cross-validation look clean and accurate.
To extract signatures from GEO, you could use GEO2Enrichr. Then calculate the differential expression of tissue-specific libraries in Enrichr. Also, you could submit gene list to Enrichr's Crowd libraries and find GEO entries with a reasonable number of mapped genes first.