Probably the most famous landmark in Montmartre is Sacre-Coeur, a Roman Catholic church completed in 1914. Put on your comfy shoes and make the trek up the 270 something stairs to get an amazing view of Paris. Rumor has it, there is a funicular you can take to the top but I have never seen it (because I’ve never looked for it). I have always just sucked it up to the top, burning quads and all. If you are able to make the trip on foot, I recommend using one of the stairs on the side of the church. In my opinion, it’s a prettier climb plus you get to avoid all the pickpockets and scam artists at the foot of the hill.
Montmartre is made for exploring, but just be mindful of your surroundings especially in really congested areas. No, you did not drop a ring, and don’t let strangers put any bracelets on you and you will be fine.