I'm going to need an enclosure with a "window".
Cutting a hole in an ABS box and gluing a sheet of acrylic over it will do, but are there any tricks to make it look really professional?
There are nice enclosures available with clear lids:
I used one of these in a project where I had an LCD, but didn't want to make the effort to cut a perfect square hole in a standard enclosure. If you don't want the rest of the contents of the enclosure to view, you could use paint or adhesive vinyl on the inside of the lid to mask off all but the section where the display is mounted.
You can buy several designs of enclosure with an aperture for 16x02 LCD displays. But other sizes are not easy to find. I looked for enclosures for 128x64 GLCD recently but found none.
How important is the "professional look"? Some commecially available equipment uses the enclosure suggested by @pert. I've used it, drilling holes for attaching the display from inside. Very practical regarding light rain etc. when moving during short time.
There is an example of an Lcd 1602 display in a box with a transparent lid here:
https://forum.arduino.cc/index.php?topic=490392.0
I like how the fully transparent lid enclosures showcase the electronics inside, while still protecting them. I like for people to be able to see the circuit board and wiring I created.
You can get escutcheons for standard 16x2 etc displays, which can cover a multitude of sins. I recall they are quite expensive but probably cheap compared to laser cutting plastic lids. I have use electrical boxes with transparent lids. The size and cost is about right but modifying them is quite tedious.
See these three post:
Post #184
https://forum.arduino.cc/index.php?topic=445951.msg3142275#msg3142275
Post #331
https://forum.arduino.cc/index.php?topic=445951.msg3335644#msg3335644
Post #132
https://forum.arduino.cc/index.php?topic=445951.msg3128976#msg3128976
Thanks all.
@LarryD You may be my new lateral thinking hero!