Information Gene HBA2
You mention that you "started in bioinformatics", so perhaps you might feel more comfortable taking such an approach to better characterize where the promoter for HBA2 might be.

As @Bitwise mentioned in his comment, "the promoter" is not a well defined region. Often times "we" take the promoter of a gene to be some arbitrary (2-4) kilobytes upstream from the TSS. With more high throughput data coming online (especially from ENCODE), we are starting to get a better picture of where the functional regulatory elements of genes might be.

By combining data from several different high-throughput assays across a variety of cell types, the human genome has been segmented into broad regions of interest. You might start by looking for where the "Predicted promoter region including transcription start site" segment is for HBA2.

I'd also take a closer look at the DNase-seq data in this "promoter region" across as many cell lines as they have processed for you to look for regions that are differentially occupied in hopes of identifying more precisely which parts in the promoter region might be important for the gene's expression (this would, of course, require you to connect DNAseq data with gene expression (RNA-seq) data).