I did some investigation myself recently after my uncle asked if I would build him an arcade machine with coin slot for use in his pub.
First thing I did was check out the license that comes with the arcade compilation games, like Taito Legends and Namco Museum. It seems that these all have the same "private use only" license and there is usually a notice on the box, or in the instructions that states "not to be used for pay and play".
I contacted Namco, Taito and some other companies to find out more and to ask for their advise, and erm, not surprisingly, I never received a response.
I had a search around for public domain roms. PD roms can be used legally in a pay to play environment so long as the owner has a gaming license.
I found a site here with a limited selection of roms.
https://sites.google.com/site/jbrodack/There are no all time greats

. If you want legal for public use then this is about your only option.
You also need to check licenses for your operating system and emulation software are valid for public use.
BTW - There are lots of other emulators besides MAME.