There was a point that crossed a line where consoles were as good or better than arcade games. I feel sad that the arcade didn't maintain that edge over anything you can do at home and it looks like most of you were born after that time. Now arcades are like the carnival rides that pop up in mall parking lots. People still go to them, but they are sad shadows of their former selves.
But I can still remember the golden days 
You can buy an arcade game machine that is "generic" (i.e. has the screen, and has a joy stick with buttons) and you can put a computer in it that has 100s or 1000s of arcade game ROMs. My old work had one in our break room. You will likely want to find an arcade machine that has at least 3 buttons though for each joystick. I don't know the specifics behind how it worked, but I imagine it can't be too hard to find information online about it.
The late 80s and early 90s are when I was exposed to arcade games, and the consoles were already starting to play the same games at this time (the arcades still had better graphics, but almost all these games were on consoles at the same time, or shortly thereafter). Also having to put in money every time you died was not as forgiving as starting over for free on a console. Some of my favorite arcade games I remember though, were:
Super Off Road:
Narc:
Rampage:
Gauntlet:
Operation Wolf:
Golden Axe:
Street Fighter II:
NBA Jam:
Mortal Kombat:
Even up til the late 90s or even possibly early 2000s they were still coming up with good shooting arcade games (like Big Buck Hunter, and these games below I loved like Time Crisis and the sequels, Silent Scope). A local pool hall had an old school shooting game with 2 plastic pistols that just featured certain games of skill, I don't even know what the name of it was. And I was playing Golden Tee arcade game from probably 2001'ish up until close to 2010.
Time Crisis:
Silent Scope:
