I will be going to Moab for 2 days next week. We are both in our 70s and are not particularly vigorous hikers. I assume there are great vistas in Arches Park. Are there any particularly good and not very long hikes? Are there any restaurants we should try in Moab?

Don't expect daytime highs over 60*. Take the hike out to Landscape Arch. It is less of a climb than the longer hike out to Delicate Arch.
I liked the Moab Diner better than the other places we ate.

You can see a lot in Arches with very short hikes/walks. The trip out to Landscape is not very hard, but there are lots like the Windows and Turret Arch that are just an easy short walk. To get a picture of the hike to Delicate Arch you can go to my photos at www.flickr.com/photos/emalloy2009 and scroll down to the picture of us at the arch, the next picture shows the route. If you scroll in you can see the path below the slick rock and in the distance see the light on the cars where you park. We were mid 70s when we did it and we had to stop frequently and drink a ton of water. The last little section before you get to the arch involves walking across a ledge that is about 4 feet wide with a wall on one side and a drop off on the other. The hard part comes when people going the other way won't let go of the wall and you have to scoot around them on the drop off side.

Have you searched for Moab posts here? There are many of them with ideas for exactly what you want. Hit the Moab Visitors Center for info on hikes and restaurants.

Suggest night Colorado River boat cruise
Brilliant boat lights illuminate canyon walls
No rapids

Restaurants - there are two micro-breweries in town with excellent lunch menu
Dinner:
Best view of Moab and landscapes is an early dinner at Sunset Grill located on a very high hill.
Originally the home of Steen who discovered almost pure uranium ore locally
- google it.

435 259 7146
Vaga

Except for Delicate Arch and Double Arches, and the ranger guided hike, the rest of the hikes are very easy. Moab Brewery for casual, desert Bistro for more upscale and Sweet Nothings for breakfast or sandwich to go are my restaurant recommendations