The best way to sound proof a exterior wall
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There are acoustic tiles make to attach to walls to help sound proof.
Double pabe windowed and good installation between the studs should do it
Most noise is transmitted through the window, so heavy drapes (like heavy velvet) and cellular shades help. Then to do whole wall, I would do rigid sound board.... https://www.homedepot.com/s/rigid%2520sound%2520board%2520insulation?NCNI-5 you could cover the panels first with fabric using spray adhesive so their not ugly, and then use doubled sided foam tape to attach to the wall. I get that double-sided foam squares at Dollar Tree for lots of projects.
I'd look into having some soundproof tiles applied to the wall