It all depends on what you're looking for. If you are wanting to just get out and find coins and possible jewelry, the local parks will work just fine. Your coin finds will probably be of the modern type though, but you never know. This is where most of the "trash" will be though. Or in detecting terms, anything made of metal which you usually don't want such as pull tabs, foil, bottle caps, etc. Also, if you want to detect the local parks you must get a license from the parks & recreation office. It's not much, only $5 for a year. But one thing they do not tell you is that you are only able to dig with a probe. A shovel or spade of any sort is not allowed! I'm not a big fan of that rule!
Now if you are looking for older coins and relics, then start researching old homesites, battle sites, ghost towns, old roads which no longer exist, old footpaths, etc. You can start at the Great Falls library which has old documents & newspapers on their third floor if I remember right. Plus there is the History Museum which is several blocks South of the library. They have some good reading there too. But the number one place you should start is right in your own backyard! You never know what you'll find by just searching your own yard.
If you're still stumped or getting frustrated, I would be willing to help. Right now I'm working on new places to detect since the weather is so cold and the ground is frozen solid. Let me know. Good luck!