N.M.
Hi A.! I live in Euless, and we have several free indoor play areas around here located in churches. There is one called The Cube, at Compass Christian Church in Colleyville, that's open, I think, every afternoon at 2:30. Paradise Pond, at First Baptist Grapevine, is open each Thurs. and Fri. from 9 to 11 (though it does cost $1). The Treehouse at Glenview Baptist, which is in Ft. Worth (off of 820, near Haltom City) is open the first, third and fifth Monday of each month from 10 to 12. Kidztown Treehouse, at Church on the Cross in Grapevine, is open every Friday from 10 to 11:30. And Irving Bible Church also has an indoor play area (can't remember the name of it) which is open basically all day, every day.
Other than that, I'm sure there are some other play areas near you. We have a place called Leapin' Lizards (in NRH), and in Colleyville there's a place called Going Bonkers. Those both cost $5 or $6, I think. I'm sure there are similar places closer to Arlington, though.
Hope that helps!
N.