Gymnasium is a Latin word (with origins in Greek), and its plural in Latin is gymnasia. But gymnasium is an English word when English speakers use it, so we can pluralize it in the manner of our own language. Most writers understand this, and gymnasiums outnumbers gymnasia by a ratio of about 100 to one in current news sources.
Examples
John McCain was packing the gymnasiums pretty well too. [Los Angeles Times]
Here we see a world of two gymnasiums – Average Joe’s and Globogym. [Telegraph]
Most of the events are now held at larger venues — churches, school gymnasiums, libraries and community centres. [CBC]
For the first time in decades, courts are being built across Australia instead of being replaced by apartments, car parks, gymnasiums and shopping centres. [Sydney Morning Herald]
I set out on a tour of some of the area’s smaller gymnasiums to get my proper dosage of hoops . . . [Washington Post]