I have an inexpensive watch that I purchased in Japan. It has sentimental value. I lost the back, and several repair shops have said they can't help. Can someone recommend a repair shop?

Try the links. Casio has two distributors for parts.

MANUAL ' PRO TREK - Mens Watches - CASIO

https://protrek.com > asia-mea > support
WATCH MANUAL ARCHIVES. Use this page to download a copy of CASIO watch manuals in PDF. To download a PDF file, enter the four-digit (or three-digit) module ...
Missing: movement ‎' Must include: movement

Buy Parts - Casio Support Page ' Casio USA

https://www.casio.com > support > buy-parts
For end-users looking to purchase Casio watch bands and watch parts, please contact one of our Parts Distributors* below: West Coast PacParts, Inc.
Missing: prt500 ‎1376

Casio ProTreck PRT-500 Please Help - where do the springs ...

https://www.watchuseek.com > ... > Casio G-Shock
Dec 10, 2013 - Hi there! After finding my old PRT-500 in a drawer I took it to a shop to replace the battery. They messed it up, the watch displayed "open" ...
Casio PRT-500 issues/ watch to replace it - Watchuseek
Jul 11, 2008
CASIO PRT-500. Please HELP ME. - Watchuseek
Oct 10, 2006
More results from www.watchuseek.com

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do a search for a watch repair shop in your area

try this site:
https://oureverydaylife.com/how-to-set-my-athletic-works-watch-12234179.html

Some watches the back screws off some have to carefully pry the back of with a knife. Once in look for anything that holds the battery in. Carefully remove the battery and check the number on back for replacement. If it has anything holding the battery in place it is easy to break. If the watch is expensive or has sentimental value take it to a watch repair or a jewelry store for replacement.

Take it to a registered Rolex dealer it may cost a little bit more but it will be worth it in the end and it will be done by a professional, hope this helps, Paul.

value is only what someone would want to pay for it at that moment. Sentimental has no market value...

nothing available in a brief internet search. I would take it to a watch/jewelry shop for inspection/insurance evaluation. Understand insurance/replacement value is always more than actual street value

replacement bands can be found on amazon, take a look here: Amazon com armitron watch band. I hope this was helpful. Cheers

The exact cost will vary depending on the shop you bring it to, and the overall condition of the watch. If the battery has just run out, it could be a very inexpensive fix ... but if the battery has died and corroded within the watch, it could be a much more difficult task, and cost a bunch more. If you are able to do so, I would recommend switching out the battery before you bring it anywhere as doing this yourself can save you some money and might get it running again in no time. As for replacing the face, I would recommend taking it to a repair shop for this (though once again I am not sure how much it would cost ... it depends on how much of the watch has to be taken apart to get the face off).
If your watch relies on a wound spring rather than a battery, then you would have to bring it to a professional to get the spring fixed (if that is why the watch has died). This is a delicate procedure, and requires a bit of skill and knowledge about watches to get it done right. This would be a bit more expensive to fix, but if your watch bears a lot of sentimental value, it could be worth it. If you have to wind the watch daily to keep it running, and winding it no longer works, then you are best to take it in to a repair shop and ask for an estimate.

I'm afraid you have to visit clock repair shop, as without close inspection it is not possible to say what's wrong with your clock.

mcdevito75 here, Hello Dave, My advise is to take your lighter to a jewelery shop, you can try a small place, they may have the info or even repair your lighter. Also try Colibri watches.com try and see.