There's a place called Jumping Party in Arlington (www.jumpingparty.com) that is an indoor inflated bounce house place. My son walked when he turned one so I went ahead and took him. He loved seeing all the other kids and bouncing around... and they let you, the parent, go on the 'rides' with your child if they're small, so that's nice.
You could try the Botanical Gardens in Ft Worth, but then again, my son is an out-doorsy type of kid, so I don't know if yours would love it like mine did.
Legacy Park on Green Oaks has bike trails for miles if you and your husband enjoy that sort of thing. You could put baby in a bike seat or bike trailer and have some fun that way. Or put on some roller blades and push baby in the stroller. There's a park and lots of room for the baby to run around and play, too. If it's a windy day, you may see people out flying kites.
I think that's all I got for a 1 yr old. Hope you have fun!!