there has to be some give and take.

I agree, if the girl sits back and puts no effort in the relationship will be a dead end. But

isn't it also on the girl to do the same?

I don't really agree with. And

He should suggest they try to settle into a back-and-forth date night-- one weekend it's her pick, the next weekend its his

I really disagree with, because this is rationalizing, sitting down and making a schedule and trying to recreate the attraction, tension, and all that stuff that makes a relationship awesome-- and this doesn't work, because it's about feeling, emotion, gut reactions. Sitting down and making a schedule is exactly what you should avoid.

Apart from that, I think the girl should make other efforts than this-- taking charge in actions and decisions is a man's effort.

I realize I'm slightly oozing into RedPill territory a bit here, but bear with me ;-)

Although men and women are equal and should be treated equally as human beings, I think underneath there's lots of differences, and one of those differences is what sparks our imagination, what attracts us in the opposite sex, what excites us. This is on a subconscious, built-in, gut-feeling level. There's a reason almost every romcom has the same basic premise. :-)
I think girls like to be 'swept away', for her guy to pick her up, and regardless of some practical or logical objections to take her places. (Hell, who doesn't-- I'd like it if it happened to me.) Apart from that, a girl likes to feel that her guy takes care of her and protects her.

I think guys like to be challenged, teased, seduced by a girl, and secondly be loved, supported and cared for.

You might see this as sexist, but it really isn't-- it's how it works (for most, anyway). And I'll emphasize: this has nothing to do with inequality on a broader level, because women should be treated equal in the work office, earn as much as the guy doing the same job, and get the same amount of respect as men for their achievements.

So what can a girl do to spice up the relationship? Challenge your man more, tease him, seduce him like you did in the beginning. And yes, that means looking into new clothes, make-up, ways to be more sexy and seductive. Shallow, maybe, in the same way a guy might hit the gym so he'll be stronger and more able to protect the girl. There are exceptions, but most girls find guys who are a little fit more attractive than their potatoe-shaped counterparts. ;-)
Secondly, you could your man a special day or evening full of attention and care, this can be all kinds of stuff. This can be taking him out to a restaurant that has his favorite dish (or cook it for him), taking him to a sports game he loves, treating him to an evening of relaxing at home or at the cinema- and when you go out, making an effort to look at your best for him.

Again, this is nothing logical, equal or rational, it has nothing to do with sexism or disrespectfulness-- this is pure gut feeling. It's the stuff that gets blood circulation going.