Best place to do this is during the Midtown Patrol while going for the
Part-Time Hero achievement. There are venders (same venders you find at Avengers Tower and every other base) at the initial spawn point of the patrol, and while you are out beating up enemies in the free roam area you will get a lot of useless loot, which basically becomes vender experience via your donations.
After doing the patrol last night for less than an hour I had bumped a vender past level 4. It is a grind, but going for civilian rescues is a grind as well - no reason not to kill two birds with one stone here.
You can speed this up by either obtaining the Kingpin Medallion (drops credit cases) or the Tombstone Medallion (drops various items - gold watches, necklaces, wallets, etc) - these can be used to donate and rank up a vender even faster.
Questions, corrections and neg vote justifications below.
EDIT: As of 11/27, the MHO servers have been taken down and the development team is in the wind. This, as well as all achievements, are now discontinued.