Here are some thoughts about stroll and saunter, and still another word, amble: http://www.englishforums.com/English/StrollSaunter/cgmng/post.htm ramble connotes walking around aimlessly, without any particular destination. To me, ramble indicates extreme disorganization. (ramble also means to speak with many digressions and in a very disorganized way. "The old man is a bit senile, and just rambles on about his youth.") roam means to travel here and there over wide areas, but the traveler may have a purpose and a direction. And don't overlook the word "wander" which also means to travel aimlessly. Please look here for further explanations of some of the words we've mentioned, and other words, as well, along with sample sentences: http://www.thefreedictionary.com/wander

"Wander" is when you are lost, you have no idea where you're going, unlike "roam". Ex: "The state is urging gamers to be more aware of their surroundings after two people wandered into a heiau while hunting for Pokémon Go". To me, the main idea is that these two people strayed. In a recent article, the headline says "Thousands Set To Roam The Streets For Tomorrow Night's Pokémon Go Crawl" - Clearly, they deliberately travel the streets and its wide areas.