It seems like, throughout the internet, there are three main options. The three options are the Ballroom Blitz (Pyro Pete's Bar), the Race (Tier 3), or Slot Machines.
Here's a video explaining the Ballroom Blitz:
Essentially, from what I found from the GameFaq forums:
Bar room ball. Tested and it's faster. The quickest I was able to get
20 from the race was 80 seconds or so. 1:45 to finish the race and I
had something like 20 seconds left over. Bar room brawl on the other
hand, you get 2:30 (I think) and the fastest I was able to do that was
in 45 seconds. The trick is to stay in two areas. The Badasses only
appear to spawn upstairs and out of the top right door on the bottom
level (according to your map) so all I do is stay close to that
staircase and travel up and down between floors. Never have I failed
to kill them all this way and usually it's in under a minute.
On the other hand though, you can try doing the races to gain tokens. It's a lot simpler if you have Afterburner relics with you.
Also taken from the GameFaq Forums:
Bar Brawl is faster ... but I HATE that I lose money there. Every
session at least one or two rats seem to get away and stash my money,
So I just used the Tier 3 Death Race with an Afterburner relic. Only
slightly slower, but no irritating money loss.
Note that with the option of doing the races, you will have no rats taking your hard-earned Torgue Tokens, and you'll get a guaranteed 20 tokens upon winning.