Trip to Houston staying downtown

My (37f) and my girlfriend (41) are coming down from outside Austin to go to the Yankees Astros game early July. We will be there Thursday-Sunday. Friday before the game we are going to natural science museum.

After that we don’t know. I wanted to take the Port of Houston boat ride but they won’t be open until August I think is what I read. Is there a place you can go and overlook the port and watch container ships come and go? We both are fascinated with huge ships mostly me.

Also, we want to go out to dinner to a casual but nice restaurant with good food. We love Lockhart BBQ so we may find a bbq place in Houston to try. Last time we went out I had a chicken salad she had country fried steak so it’s not like we have expensive pallets lol.

What would be free or cheap to do on the weekend? I’ve already spent a pretty penny on this trip and I’m trying to keep the rest cheaper on the pocket book. I’ve searched Google and they just talk about all the parks. I have no idea what people’s fascinations with parks are. Seeing downtown skyline sounds cool, but that’s about it.

Would love some ideas to help make this trip even more awesome.