I've never caught a gar or a dogfish. I would like to add it to the list this summer. Where would be the best place to fish for them? Northeast Wisconsin is "local" for me and I'd prefer not to travel too far, but I'm not opposed to that either. I just want to catch one of each.
I want to catch a dogfish and a gar
When I lived in Stevens Point, a friend took me to the backwaters of the SP FLowage. He told me to clean out my tackle box of all of the dud lures that I had and bring them along. The dogfish were on their beds for the spawn. All you had to do was get a lure near them and they'd attack it. Shallow weeds were the ticket and I think it was late spring/early summer. Check to see when they spawn. They are very aggressive and a blast to catch.
Here is a vid of a guy making a rope lure and a goofy contraption for after you catch one. You would really have to catch a lot of gar to make that worthwhile...
https://www.youtube.com/watch?reload=9&v=gB9gtG9X5JE
Around 35 years ago when I lived in the Wausau area I used to target dogfish on purpose in the shallows of the Eau Claire Flowage. I used Tiny Torpedos and other small floating baits that could be twitched in the open pockets of the weed flats and up in the backwaters. It was always a little creepy when you would get them up in the boat and they would start barking, but they fought like beasts and the hits were explosive.
Mid-summer Mississippi River backwaters are full of Long Nose and Short Nose Gar. I hard part is getting a hook to stick in that narrow beak. A piece of cut bait, with a short section of soft nylon rope that is frayed, will work very well. The cut bait will bring them in and the rope gets tangled in their teeth, so they will not fall off.
Fish one of the flowages and in Late May Early June to catch Dog fish. Jig and Minnow just like you are targeting Walleyes. We catch them on the Willow and Nokomis during this time frame. Catching Gars is a different animal I can't help you on that. Shoot them with your bow.