Is possible to find one furnished studio to rent 3 months either Rosarito or Playa del Carmen? Yes. But maybe in that short time will be more expensive and hard to find. Maybe it will be better to stay in one cheap hotel?
I guess for you will be more easy to find an apartment in Playas de Tijuana.
Now about the cities:
Rosarito is small community in Baja California, more focused to retired expats from USA.
Playa del Carmen is a hot tourist spot south of Cancun and attracts thousands of tourist from all the world daily.
which one you think will be more expensive? and fun?
My recommendation is that you spend a few days in Playas de Tijuana and see if you like it or not, you ask for rent prices and the same in Rosarito and Playa del Carmen, there is really no other way...