These areas have worked for me in generally avoiding hot weather, though some can have days between 80F and 85F--one hopes not too frequently.
Iceland (obviously, though I've not been there and it could be cooler than you want)
United Kingdom (especially Scotland, whose west coast can be wet)
Ireland (another place I haven't been, where I'd allow for wet conditions)
Norway, Sweden, Finland (too expensive to be seriously overrun; western Norway can be wet)
Estonia, Latvia, Lithuania (capitals get considerable tourism, especially on weekends)
Netherlands and Belgium (heat waves more likely here, but not a frequent occurrence; can be wet)
Normandy and Brittany in France (can be wet)
Northern coast of Spain between Galicia (west) and Basque Country (north) (can be wet)
Places at considerable altitude anywhere
Maybe Denmark, far northern Germany and northern Poland (not enough personal experience to be sure)
There are places in the UK that are very touristy, starting with London, Edinburgh, York and Bath, and in the Low Countries Amsterdam, Brussels and Bruges get heavy touristy traffic. Attractive coastal cities nearly anywhere may have multiple cruise ships in port on some days, which can be obvious when the city is rather small, like Bergen. But other cities in the same countries won't be so heavily visited except, I guess, beaches in the summer. Keep in mind that Europe is a lot more densely populated than the US, so large cities will have lots of people out on the sidewalks--though most will probably be locals rather than tourists.
For vetting likely weather conditions at destinations you're considering, I highly recommend visiting a website like timeanddate.com, where you can find actual, historical, day-by-day weather statistics going back a number of years. That kind of data is much more useful than monthly averages in providing a good idea of the range of conditions you may experience.
Stockholm weather -- July 2025
That's just an example; always check multiple years (I like 5 years), because weather can vary a lot. Use the pull-down box at the right, just above the graph, to change the month and year displayed. Use the Search box at the upper right to see data for a different location.