Door County is nice, but it depends on what type of experience you are looking for. For my taste, Door County in July would be too crowded, and generally too "touristy". Since you like to hike and fish, you might want to consider some other places in the Northwoods of Wisconsin - like Eagle River, for example. Or, just west of that area, check out towns such as Boulder Junction, Minocqua, Manitowish Waters - all interesting places, especially if you enjoy outdoor activities. Many lakes in that area with good fishing, and plenty of places to hike on the Chequamegon-Nicolet National Forest. If you want to see Lake Superior, you could head up toward Ashland and the Bayfield Peninsula (Bayfield is very scenic).
July or early August would be the time to visit, if you want warmer weather (and fewer mosquitoes than June).