Honeymoon Ideas help (on a $5K budget)

As a planner, I prefer to make my own itineraries, line up tickets, book lodging, etc. instead of going through any service or agent. Our budget is max $5,000, but lower would be better. Looking at likely about a one-week timeframe including travel (Saturday wedding, Sunday departure, Saturday return). I want something that feels nice, not having to skimp, but stays in our budget.

I'd like to have the honeymoon immediately following the wedding (May 2023 or 2024), but willing to wait to hit the best timing.

My priorities:

• swimming
• hiking (with waterfalls) – for casual, amateur hikers who can handle a little incline
• spa day
• sightseeing of some kind (art museum, ruins, historical site, other museums, etc. – no plantations or war/military stuff)
• culture/entertainment of some kind (concert, zoo, aquarium, tours, etc.)

His priorities:

• avoiding crowds/people
• trees and the outdoors
• hotels or resorts only (no B&Bs, AirBnB, motels, etc. A cabin with amenities could work though)

Definite no's:

• camping
• cruises (seasick)
• winter holidays/activities (skiing, snowboarding, snow, etc.)
• heights (hot air balloons, for example, or bungee jumping)
• Disney

My original idea/plan was Greece, since I've always wanted to go there. But the flights there and back eat up so much time and money from the budget. Once I finished the list of everything I wanted to do, it seemed best to save that trip for later.

So far my only backup is Acadia National Park/Bar Harbor, Maine. The main downside is the lack of significant cultural spots or entertainment. I know America can't compete with Greece, but a large art museum or living history site would be nice. They have ghost tours, but I'm wondering if those might feel a bit tacky/touristy.

I'm avoiding California and other far-west options due to travel (we're in Indiana) and budget. Avoiding Florida because my experiences were usually muggy and crowded, two things my partner can't stand. Also, the FL lodging/resorts I have looked at were expensive.

Also ruled out:

• Jackson Hole (too Western/rugged)
• Mackinac Island (too expensive)
• Hawaii/Puerto Rico/Virgin Islands (too expensive with flights)
• New Orleans (too urban)
• Austin area (too many memories with my ex)
• Savannah (muggy and crowded)

I'm considering Gatlinburg/Pigeon Forge/Smokies area. I've been there a few times with family and it's a solid choice, but part of me wants to use this opportunity to go somewhere new.

A New England road trip is also an option, but it's a little overwhelming figuring out where the must-see stops are for one week on the road.

Any suggestions?