Clockwork and Automata

Papa Joes Biersalon in the Alter Markt section of Cologne.
https://www.atlasobscura.com/places/papa-joes-biersalon-klimperkasten
http://www.papajoes.de/about-papa-joes/
Old time musical automata, plus live music and Koelsch Bier.

I just looked in search engine and found a long list of possible museums specializing in automata, musical devices, and period magic and illusions. I did not find a curated or centralized listing of European museums, but certainly such must exist. Most of the museums have contact information on their sites so you should be able to ask the proprietors for additional references.
This is a database of music box museums and a large collection of links that might take you interesting websites:
https://mbsi.org/museum-list/

If you are in England you might like to visit the Royal Observatory in Greenwich and see it’s famous collection of clocks, including the Harrison clock. https://www.rmg.co.uk/stories/clocks-timekeeping

Yesterday was the 199th anniversary of Babbage issuing his "difference engine" paper. Though he never finished building it, the Science Museum, London has some parts of it. There's also a modern build of his No 2 engine design.

In Salisbury Cathedral they have the world's oldest working clock (though some envious places dispute this and wrongly claim their's is older).

There is a famous C18th automaton at the Bowes Museum in Barnard Castle.

On your wider pre/early industrial interest, around Britain you'll of course find many examples of early industrial mechanical devices that have been preserved or sometimes rebuilt.

Any particular era? One of the (IMO) most interesting examples is the Antikythera mechanism, currently on display in Athens.

The astronomical clock in Prague also deserves a mention. As well the many cathedrals all over Europe with impressive clockwork in the tower. And smaller churches as well. I once got a very interesting tour of the tower and the clockwork at a small church in Oxford.

Here are two musts - The clocks and scientific instruments at The Zwinger Museum complex in Dresden - https://www.der-dresdner-zwinger.de/en/the-dresden-zwinger/ and The Arts et Metiers Museum in Paris - https://www.arts-et-metiers.net/ One of the highlights there is the musical automaton of Marie Antoinette playing a hammered dulcimer . https://www.arts-et-metiers.net/musee/automate-joueuse-de-tympanon

At the Copenhagen City Hall we saw Jens Olsen’s World Clock. Magnificent workmanship. One of the clock’s gears completes one rotation every 25,753 years. https://en.wikipedia.org/wiki/Jens_Olsen%27s_World_Clock

I almost forgot one of my favorites - The Kunsthistoriches ( Art History ) Museum in Vienna . The Kunstkammer section is for you - https://www.khm.at/en/visit/collections/kunstkammer-wien/selected-masterpieces/

Also , since you indicate early industry , Derbyshire ( Peak District ) and Ironbridge Gorge in Telford , England are also very worthwhile . more information here - https://en.wikipedia.org/wiki/Derwent_Valley_Mills and https://www.ironbridge.org.uk/

I'm surprised that nobody mentioned https://www.museumspeelklok.nl/lang/en/ The Museum Speelklok in Utrecht in the Netherlands. It used to have a real tonguetwister name but they've shortened it. It is just the sort of thing you're asking about - I spent about 3 hours in there once. Don't know what it is likely to be like post-pandemic but they used to take you around and make many machines operate. Both educational and fun.

There is a famous C18th automaton at the Bowes Museum in Barnard Castle.

Isn't that just for checking eyesight?

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But seriously folks, I think that the reference is to the Silver Swan - a most incredible machine the like of which you will struggle fruitlessly to replicate in your travels.

Just remembered another jaw dropper . A bit north of Paris , the Astronomical Clock in Beauvais Cathedral - https://en.wikipedia.org/wiki/Beauvais_Cathedral#/media/File:Picardie_Beauvais4_tango7174.jpg

Visit Rüdesheim. Siegfrieds Musical Cabinett is a joy and so much fun. Where else can you hear a group of violins playing automatically? All of the old circus calliopes are great too.
https://www.smmk.de/pages/en/welcome.php

This video will BLOW YOUR MIND " The fantastic world of the greatest creator of automata in the world " Spend a half hour with this , you will be enchanted https://youtu.be/i3hPpcJNK_s . Also , my wife just reminded me of The Peacock Clock in The Hermitage in St. Petersburg , a short video - https://youtu.be/0A5FeaD3iwA Also , as I had previously mentioned , The Marie Antoinette dulcimer in Paris was shown at The Metropolitan Museum in 2013 where I first saw it . Only several years later I encountered it again in Paris - https://youtu.be/nITEU4fsqCU

Thanks to everyone for the good suggestions. I’ve been to a few of these and others are on my list, but there were a handful that were not on my radar, so much appreciated. Since no one has suggested a single source like a guidebook, maybe that’s a void to be filled?

Although the Utrecht museum is on the link in the second reply, that list did not include the hand-built massive clock (and associated workshop beside it) in Lier, Belgium.
https://en.wikipedia.org/wiki/Zimmer_tower

It's not worth an extra plane flight, maybe, but it's easily reached from the popular cities in northwest Belgium, with frequent local trains from Antwerp. Lier is a very attractive medieval town center, with lovely canals, and a few other small museums, like the town's art museum, and a doll or puppet (?) museum that I didn't go to. You want to try the local pastry, Liers Vlaaike. It's conceptually similar to a pecan tart, but I think without any nuts. (Not a medical promise!) Lier combines well (for train line reasons) with Turnhout (no clock museum), which has superb wood carvings in the Cathedral, and a nice little Beguinage.

I see online there may be a clock museum in nearby Mechelen, (also a great medieval daytrip). I think the weekly market day in Mechelen is Saturday. Mechelen can be reached by city bus from Antwerp, as well as by train. When the early cloth trade faded elsewhere, Mechelen was briefly the third largest city in Europe. That's hard to believe today.

There is seldom access to the mechanisms, but I might note that Belgium (and Mechelen especially) is noted for carillons.