For US passport holders, 3 months is required beyond your planned date of departure and 6 months is recommended beyond your planned date of departure from the Schengen area. Tourist visas are not required for stays of less than 90 days. For more info: https://travel.state.gov/content/travel/en/international-travel/International-Travel-Country-Information-Pages/Iceland.html
Tony and Liz have created a Google Map with some of their favorite places marked. Check it out here: https://www.google.com/maps/d/u/0/edit?mid=1_9AUHKkfcZ_K-5v5I_O1AZ9LFiQrhzOA&usp=sharing
We’re working with wedding planners Pink Iceland for our wedding adventure in Iceland (https://www.pinkiceland.is). If you plan on extending your stay in Iceland, feel free to get in touch with them about your travel and accommodation needs. They have a dedicated team of people organizing, advising on and booking tours, activities and accommodation. By using Pink Iceland you get to deal with a real human being who will give you their honest advice, based on experience and provide an insightful, intimate and off the beaten track itinerary for you. Pink Iceland travel planning services start at 50,000 ISK (approx $390).
Our wedding planner is also a travel planner and has a list of some top travel tips and advice here: https://www.pinkiceland.is/pink-advice