Why would the spend $350 to stay in Orlando if they aren't doing any of the parks? that isn't that cheap for 2 people. Why wouldn't they take that $350 and stay somewhere that you don't need an amusement park as the reason you go to that locale? And they have to eat for a week.
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I do many vacations at WDW without buying park tickets. I love the parks and would love to have an AP every year but I can't and don't. I wouldn't be able to go as much with regular park tickets every time.
And have a wonderful vacation.

Love simply hanging out.
Plus, other places cost a lot more than people think. Niagara Falls, for example, is insane for food prices.
So here are some of the things I do on the cheap just at WDW.
Not that they need many - it is their honeymoon 
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Sorry in advance for duplicates.
*time at BW
*drinks at BW - the Screen Door sells airport bottles of rum and bottles of coke - mix and enjoy if even drink prices are too much for them - if they drink
*nightly entertainment there is wonderful
*bike rental
*BW Bakery is not expensive and can be shared and just sit out and enjoy the ambience
*the pool bar at BC's SAB is open to everyone - relaxing area
*movies on the beach at BC
*ESPN for a game night if they are into the NBA playoffs/NHL playoffs
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*time at FW
*many free activities
*nightly movies middle of resort - outpost
*marshmallow roasts
*beach there
*sport rentals
*bike rentals
*Trail's End never advertised this but they used to have the buffet available for takeout - they give you everything you need - take it to the marina/beach - one takeout could easily feed two
*
the CR/WL/FW boats - the small ones are one of my favourite parts of WDW - hands down - warm night lovely choice
*stop at WL - takeout from Roaring Forks to outside tables - ambience is lovely there - or pool bar
*Electrical Water Pageant at any of these resorts
*WL has many terraces - front and back of resort on many levels
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Animal Kingdom Lodge
*loads of free activities there
*just exploring the lodge and Kidani is wonderful
*night vision goggles
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DD
*boat up to POR lovely - POR is a lovely resort to take in - eat outside
*rent bikes at POR - over to POFQ or walk the pathway
*free chocolates at Ghiradelli's
*someone told me that Ghiradelli's has a sundae coupon deal.

*take in the ambience of DD and entertainment
*Cookes of Dublin has a lovely outside eating area
*POR has some nightly entertainment in their lounge
*boat from DD to OKW is lovely as well - as is walking around that main area of OKW
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Polynesian
*watch Wishes from the beach
*take small boat to GF or MK
*breakfast at Kona Cafe is good, if in budget
*but takeout for Captain Cook - nice outdoor seating (under construction??)
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Grand Floridian
*there is a lovely terrace there - it's up the grand stairs - it's a smoking terrace but it's not if no one else is there.

It's gorgeous and peaceful. Looks out over the GF pool.
*outdoor eating area by Gasparilla Grill is lovely
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Sneak into a hammock somewhere

*they are at Coronado Springs and the Polynesian
*Pepper Market at CS can be reasonable and can be easily shared
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I agree do a day at a Florida beach - people rave about the Siesta Key area
Don't forget restaurant.com certificates
Enjoy their own resort, of course.