My step dad has put my mom in an old nursing home where they live. Mom has zero family there besides him. Any suggestions?

Why can't you invite your stepdad to move to your town along with your mom as well? That way mom can be in a nicer place and have more family around, and your stepdad can still visit when he's able. It would be a win win for everyone.
Now, just to be clear, I'm not saying to have your stepdad move in with you, just to the town you're living in, so he can be close to his wife, your mom.

Otherwise if he's not open to that, there really isn't much you can do, as he has the final say pertaining to the care of his wife.
I wish you well.

What does your Mom say about this? Is she capable of voicing her wishes? If she is capable, her wishes should be honored. If she isn't, her husband calls the shots.

Unless you petition for Guardianship your Step dad is the one that gets to make decisions for your mom.
If you have a good relationship (other than this issue) if you seek guardianship you can kiss that relationship goodbye.
With dementia a 30 to 40 minute visit is probably the limit for a good visit. You say in your profile that mom has been living with you. What or when did that change?
I am curious. You say the facility that mom is in now is an "Old nursing home" but you classify the facility near you as a "Care center"
Many "care centers" will also share bathrooms. There is an option for a private room or having a roommate and there are ones that will have a "jack and jill" bathroom. Any of these options are just fine and acceptable.
Keep in mind the cost of an "old nursing home" VS a "new care center" might play a role in the choice made.
And I have to ask have you visited the "old nursing home" and spent some time there to see how the residents are treated. Have you checked Medicare website for violations for both centers?
If mom has "never been one to sit around" does it really matter if there is no TV in the room. It is better that she is in a community room with others. And when it is time to go to bed really you should not have a TV on. (this includes all of us!)
As she declines less and less time will be spent with activities. More time will be spent in a wheelchair or in bed. She will loose the ability to interact with others, she will loose the ability to do activities. Depending on how fast her decline is this may not be many years, it could be 9, 12, 24 months.

Can you not find another facility near SD? Is he paying privately or is she on Medicaid. Who is going to pay for a a facility with a private room? You know half their assets are his.

You may want to talk to a lawyer about how Moms and SDs money can be split. SD should have done that when placing her to protect his share. Medicaid allows for splitting assets. Moms share gets spent down and then Medicaid applied for. Dad stays in the home and has enough money to live on.

The only way I can see this working for everyone is Mom and SD moving into an AL near you. Some have apartments or different size rooms. He would not have total care of her. If he wanted to go out, he knows she will be safe. People can have cars in these places. In Moms AL there was a woman who lived there with her husband who was the one who needed the care. When he passed, she chose to stay. This would depend though, if they had the money. I would pick one with a MC side. This way when Mom gets worse she can be transferred over but SD will be nearby.

He is correct. His relationship with your mom trumps yours. The only you can probably get him to agree to the move your mom is to ask him to come live with you.

Have you been to visit your mother recently? I realise it isn't easy - I'm only asking, I don't mean this question to sound critical. I'm wondering if you've had a chance to have a relaxed conversation with her about how she's feeling these days.

Next: have you been to see the brand new care center? I don't think it's realistic to expect your stepfather to let your mother go lightly, and a 30-40 minute visit may be about the right length of time for both of them. But just maybe the new center might be able to accommodate both of them, and have advantages to offer stepfather too. Does he have much of a family or social network where he lives?

This is just my opinion. I think that stepdad has the right and responsibility to make decisions for her. I am sorry, but it feels cruel to think of separating them now. Perhaps that will happen in the future.

Nothing you can do unless your mom is on board.

Talk to your mom and ask her what she wants then do it.

Sge might would rather stay there and let hubby visit every day or if offered a choice, she may want to come stay close to you.

You might check the money, maybe step-dad doesn't have the money to pay for the new place by you.

Whatever happens,, buy your mom a TV for her room

Following on FunkyGrandma's suggestion, perhaps you could invite your father to stay with you for a few weeks, not only so he can visit your mother but also so you can assess his situation now.   Having moved your mother and his wife might be causing him more sadness and/or turmoil than can be realized when not in person, so this actually could address care of him as well.   

I would become as well acquainted with the new care center as well, checking for libraries, activities, food and menu choices, and everything else you can think of.

Is this an AL or IL facility?

It depends on the day. She says she wants to be close to him but then says it would be nice to be close to me and my family. She asked me to not let her die in nh, I told her I wouldn’t. Her memory and decision making is hit or miss. She tells me that the nursing home is awful and staff not so nice. When I tell my step dad my concerns he agrees but he can’t take care of her. It’s heartbreaking because they do care for each other so much but I hate she is there alone. Here she would have a private room with bathroom and within walking distance to my home. She have family, grandkids and friends that would visit and take her places ba sitting in a room doing nothing and getting weaker.