Upfront warning . . . I have only recently dipped my toe into the bioinformatics ocean, so don’t take my words as gospel.
There are tons of different software packages out there for working with sequence data. If you feel adventurous, I would suggest creating a Linux boot-up on your computer so you can install UGENE which is a free bioinformatics software package. I haven’t looked, but I would assume there are tons of tutorials on the web that could teach you how to use UGENE with real data. I would also assume that there is a variant track somewhere online that will allow you to visualize where all the known mutations are within the SARS genome.
Having a Linux boot on your computer could also allow you to go down the command line rabbit hole of bioinformatics which will scratch every geek itch you may have. There is something oddly satisfying about pasting in a massive command line into a terminal window and getting back a tab delimited file that has all the info you need. Bioinformatics software is a bit intimidating at first, but it is very satisfying when you start to understand it.
As to BLAST, it isn’t widely used for discovering variants. BLAST is used for things like annotating genomes and trying to identify which species a stretch of DNA/RNA or protein came from.