Of course, not all trans people will agree with me on all these points (in particular, a number of trans men and trans women are decidedly not on "Team Gender Neutral," and those who are occasionally sneer at single-gender signs that have a trans symbol on them), so you should consult with local trans folks when you can.
Make sure your staff--all of them--are on the same page and understand that your restrooms are trans friendly.
A few years ago our local Pride wound up a huge cluster because although they had a policy on the books that was trans friendly, not all of their staff were explicitly told about this, leading to security asking people to use different bathrooms. Even if you run a venue that you personally would expect a trans inclusive policy to be obvious, keep in mind that basically every single community out there--including lesbian and gay communities--have been pretty bad at this in the past, and there is a very vocal minority of people who are extremely transphobic. So make sure they know so that any policies are actually followed.
Get signage that isn't insulting and shows inclusion.
The vast majority of bathrooms just say "men" and "women," maybe with some "person in dress" or "person in pants" images. I am on team "go gender neutral," but there are other issues that my prevent you from going that route (based on legal issues and the structure of your building). One of my personal favorite ways of handling restrooms--especially if you absolutely can't make your restrooms neutral--is to label them with easily-understood "men" and "women" signs with a transgender symbol included to indicate that you should use whichever one you're comfortable with (our local Unitarian Universalist Fellowship and a local Goodwill go this route).
If you do have gender-neutral restrooms, phrases like "all gender" and "gender neutral" are better than "unisex" (although honestly I wouldn't be bothered by the latter).
I hate when gender neutral restrooms are labeled "family." Hate it.
Also, if you don't have neutral restrooms, can you not try and get "creative" with your signs? Most of these rely on either some sort of constructed gender role or garment, or--even worse--a set of genitals. A friend of mine and I were baffled one day to find a restroom that had the genders "olive" and "pimiento." We literally had to ask the bartender what on earth restrooms we were supposed to use. "Oh. Because you put pimientos in olives." Gross. Not to be outdone, my roommate found a worse one:
This isn't just insulting to trans people, but it's crude and insulting to other people, too.Apparently, a for-profit "co-working" space in the area has the terms "cock" and "pussy" on their bathroom doors.— Eric SilenceSchultz (@wwahammy) March 17, 2017
Oh, once a long time ago I watched some TV special on cool bathrooms (yeah, that's the kind of person I am) and it went into a club bathroom that color-coded its bathrooms... but not in expected colors, so people were constantly walking into the wrong one, and it was supposed to be all cute and social and funny, and they even had this weird thing where there would be visual contact between the men's and women's restrooms (a slit above the sink, a weird window in a stall) and although I'm sure cis people don't really think about this sort of thing, that's a great way to get a trans person humiliated, beaten up, or worse.
Don't try to make "the trans restroom," and if you have three restrooms, don't police their use.
Again, I'm on Team Gender Neutral, and wish that all-gender restrooms were a widely available thing, but since they're not in wide use, I should mention that the last thing you should try doing is making a men's room, a women's room, and a "transgender" room. This both has the potential to invalidate trans men and trans women and creates an environment where people can get outed very readily. And it's not that trans men and women never want gender neutral restrooms (not all of us pass well, not all of us consider ourselves "binary," etc.), but forcing trans men and women to use gender neutral restrooms when we qualify as "men" or "women" is insulting and invalidating.
I get it, maybe your gas station or whatnot is constantly trashed and you need at least something to keep people from destroying it, but if possible avoid locking your restrooms.
If you must lock your restrooms, try to set it up so that people don't need to seek out or interact with a staff member to acquire it. Try to avoid making it necessary for people to contact somebody over a bathroom at all. I used to have to specify a "men's 8" when getting bowling rental shoes and having to do the same for a bathroom key or some other amenity would have been at least a dozen times more awkward than that.
Also, obey the same rules above regarding signage. Don't be quirky at the expense of sensitivity.
Invest in good dividers.
One of the ridiculous things about bathrooms in the United States is that we tend to design bathrooms with massive gaps, leading to a lot of opportunities to see each other. I can remember times when kids practically crawled into my stall with me, or peeked over the wall, or did a potty dance while seemingly pushing their whole eyeball into the crack between the door and stall.
Nobody likes these. They're absurd. But for trans people they're even more anxiety-inducing, for more reasons than you'd think.
For me it was never just the looming threat of somebody seeing my crotch that made these so unsafe. When I used to bind my chest, I needed to take regular breaks to avoid hurting myself, and would regularly use bathrooms for this purpose. I've given myself testosterone shots there in a pinch. And having to do these things in an environment where people can see into the stall with ease is aggravating and makes me not want to go there.
Replace broken locks.
Lock issues are the bane of my bathroom existence.
Recently I went to a reasonably fancy sushi establishment only to find my worst nightmare: There was one massive stall, with the toilet in the corner furthest from the door, and the lock was off-kilter and impossible to keep locked. Basically, if somebody came in needing to use that stall, it would be difficult to see that I was in there and I wouldn't be able to reach the door to hold it closed. And where I'm at, I could feel comfortable saying there's somebody in there, and even if somebody were to walk in I probably wouldn't be outed, but the same can't be said for every trans person. Maybe somebody has a voice that will out them and is uncomfortable speaking, or is taking a rest from a binder without their shirt on, or the person coming in just flat out doesn't hear them.
And it's a cheap fix, too. Practically any door can have a lock stuck on the inside for a couple bucks, so why do so many businesses just leave their doors with broken locks?
Replace missing doors.
Why do I even need to mention this? There's a big disparity here, too, because when I was a woman I never saw businesses in the middle of goddamn downtown that neglected to replace missing doors on bathroom stalls, but as a man I've been places that had like four stalls and none of them with doors. One time in an extreme emergency pre-testosterone I had to use one of those and it was one of the most nerve-wracking experiences of my life, and it was a packed restroom, too. Ugh.
Anyway, these are just some suggestions for things to do and look for, and this is of course in combination with paying attention to overall accessibility.