Unique honeymoon/elopement ideas?

My fiancé and I are either going to do a courthouse wedding, then honeymoon, or elope and stay for awhile. We're looking for unique, lesser known destinations! Here's a little about us, & we'll be going sometime in June/early July most likely.

We of course would fly into a bigger city, but we usually always love the smaller areas nearby more. Like while in Amsterdam, we rode our bikes to a smaller village and fell in love with it. When we flew into Portland, we ended up loving Hood River, Oregon more.

We are definitely excited to relax, but we also love to be outside, hiking, biking, taking in the scenery. As for beachy vs. mountain-y, or colder vs. warmer we haven't really decided and are open to both.

We are also open to domestic (We're in the US!) or international destinations. Including Canada or Iceland too, not just mainland Europe.

We're not really into going out, though we'll enjoy a beer or glass of wine at a local stop. My fiancé is starting medical school in the fall, so this will most likely be one of our last big trips for several years :) We want to make it feel like us.

Thanks so much in advance!!