Well, Spokane only goes back to the late 1800's but a there are still a lot of properties and entire neighborhoods from the turn of the century. Also something Spokane is proud of is it has more public parks per capita than any other city in the country. These are many very old neighborhood parks. Most were established from late 1800's to 1930's and haven't changed much. Unfortunately they have all been very very used in their time and, of course, have a LOT of buried trash. I never have hunted them much and when I have I've never had any amazing finds but there are many.
Not totally sure how extreme they are on metal detecting anymore but I never had any issues with authorities when I went. I just made sure I did as little digging as possible. Most shallow targets can be weaseled out with a flat blade.
If you are a people-person there are many many old properties all over town so your best bet is door knocking or securing permissions. I'm not much of a people-person and not very sociable so I don't do that.
The last several years they have been condemning and taking over hundreds of houses in neighborhoods along the freeway for expansion and I and many other detectorists have enjoyed hitting those areas. That entire area was older homes so some of us did pretty well on those. Don't know how it is anymore but, like they say, no place is ever completely hunted out.
Oh, I've lived here my entire life so I do know a little of the history of the area.