The 2nd is grammatically accurate, but the 1st certainly works well enough colloquially and feels more comfortable, and in advertising the comfort of the target - the bulk of whom are not grammarians - is significant.
Also, they both leave open the implication that the "one dollar" gets you the ability to access both locations for $1 (that may be true, I don't know how it works) and it could be read to mean that the celebrator ought to be able to be at both locations simultaneously.
I'd suggest different wording altogether (and, in my example below, with the added benefit of repeating the name one more time).
"Celebrate the grand opening of Planet Fitness at either of our new locations - Planet Fitness Mason or Planet Fitness Middletown - for just $1!!!"
If brevity is not necessary:
Celebrate the spectacular grand opening of Planet Fitness at either of our new, state of the art, convenient locations - Planet Fitness in Mason with its stunning array of Spirit Fitness CT850 treadmills, or the largest collection of Bodycraft weight lifting cages in the city at Planet Fitness Middletown - all for just $1!!! (note: I have no idea what equipment they use, I just cut and pasted a google search of exercise machines.)
Okay that's a bit ridiculous. But so is advertising, right? I'm hearing the voice of a fast talking huckster in my head...