I was just in Moab for 6 nights with 90 yr. old mother and her 85 yr. old visiting friend. I've been there before, but never with this much time....it was great.
These are two amazing older women who are active and love to hike/explore, but in moderation at this point in their lives so the more adventuresome activities that Moab offers are in their past. There is a wide variety of rafting, jeeping, atv's, canyoneering and biking available with many outfitters to choose from. Lots of good information here from the destination experts.
I would also recommend the visitor centers at each park and the Moab Visitor Center is excellent.
In the past, we've done the evening jet boat ride on the Colorado, which I enjoyed a lot more that I expected to. I was being a Utah "locals snob" so was pleasantly surprised. Even the family style, cowboy dinner before the tour, that out of state friends insisted on, was a lot of fun.
I loved having an entire day to spend at each of Arches, Island in the Sky (with stop at Dead Horse) Needles District, Newspaper Rock, Manti-La Sal Loop and in town.
We stayed in a condo (VRBO) as like the convenience of our own place to wake up to and return to at the end of the day. Being older gals, the kitchen was more important than the restaurants with the ability to pack the cooler for tailgate lunches every day and no need to go out again at night. The shower, jammies, a glass of wine and dinner on the patio with view of the Moab Rim was our idea of a great way to end each day, but not necessarily for everyone, still with the enthusiasm for nightlife.
We were on the road by 8:00am and usually home by 5:00, giving us time to do the Visitor Centers in the parks, viewpoints, pull outs, 1-2 mile hikes, photo ops, tailgate lunch, chatting with other visitors and never feeling rushed.
For our Moab day, after enjoying the galleries and Visitor Center we had a great time following the Moab Rock Art guide in search of petroglyphs, pictographs and dinosaur tracks. The Potash Rd. is especially rich with rock art and pretty drive along the river.
The Moab Brewery is a good lunch stop with generous portions, home brew, reasonable prices and fun atmosphere for all ages.
With a bit of research here you'll find lots of great suggestions for all activity and income levels. It's great that you have a week. I have felt fortunate to be there for 2-3 days in the past, but the 6 days spoiled me.