Hello and welcome to the forum.
First thing you should do is make sure what you " heard " about detecting the parks is
true. You can do that by going to the Parks department and
ask. Ask the folks at the desk for a copy of the most current rules for using the city parks. Then, go the the city police department and ask
them. You want to make sure the " left hand knows what the right hand is doing ".

It's not unusual for the two departments to be disconnected with eachother.
Go to the school principal of a school you might want to detect and ask if it's OK. Practice, practice, practice on recovering targets without leaving a mess. Do that practice in your own yard. By the way, have you detected your own yard?
That's where to start your hobby.
Find a local detector dealer and ask about any local detecting clubs. That's where you'll meet folks who are " in the know " about local places to go and also the local laws.
The old Chishum Cattle Trail passes not
too far from you. Research it and look into the places where it crossed the creeks and rivers. Find out if the
state or
county owns the riverbeds or if the
landowners property lines go to the center of the waterway. That will tell you who to talk to about permission to search.
Arlington is a fairly young city, but the area is
old and participated in a lot of history. Make full use of your local libraries ( Arlington, Ft. Worth, Dallas,etc ) and study local historical info there. Join the local Historical Societies, but
do not let them know you are a detectorist. Generally speaking, " them " and " us " do not work together very well.
As I mentioned in the first paragraph; learn the rules. Then, study how to play our game within those rules. And good luck.
