I grew up in Alexandria. I detected Jones Point when I got my first detector about 1980. It was a park back then but not well cared for or kept up. I did detect there when I got my first detector. Found many coins including many silvers and some relics. Keep in mind that was with an old White's I bought at sears. I would love to try it again but they have restored the old building there and cleaned the place up and made it a historical marker. Probably off limits but worth a check. Now you could go just to the left of there under the Woodrow Wilson bridge where we used to build a fire, fish and drink beer all night and practice by detecting all the pull tabs we tossed, although most went into the Potomac. There used to be many places around there to detect but most are built over now. Any small place you can find in Alexandria has potential. I was told schools are now off limits in Fairfax Co. I will PM you a few places I remember. I moved to Falls church, then to the Sterling/Leesburg area. There was a little more elbow room there but that has filled in with people now too.
HH