Assuming from your username that you are going in as a hard navy trade, some of what I say may not apply to you.
Not all bases have PMQs.
Not all bases have gyms.
Not all bases have pools. (My base has none of these, but to be fair we are a detachment not a base).
If your base has a gym, yes it is is free for military. Depending on the base you may have to pay for family use. Still much cheaper than using a civvy facility.
PMQs can be easy or hard to get, depending on the base. They can be inexpensive or almost un-affordable. They can be very nice or butt ugly.
The best way to find out what is available for your significant other is to contact the MFRC at the base you are going to.