Recommendations for Town/Hotel close to Frankfurt May 9

You don't say at what hour you plan to arrive at FRA. Bacharach can be reached by direct RE train from the Regionalbahnhof (regional train station, one of 2 stations at FRA airport.) The train to Bacharach and beyond follows the scenic Rhine River Valley (castles, vineyards, old-world towns) for several miles once you reach Bingen. Trip takes 57 min. to one hour, with morning trains at 7:20, 9:23, 11:23. Oberwesel is about 5 minutes further. You could stay in one and visit both towns in that amount of time very easily.

Oberwesel:
https://www.weinhaus-weiler.de/wp-content/uploads/2016/08/DSC_2434_1920.jpg
https://mittelrheingold.de/wp-content/uploads/2018/07/marktplatz-oberwesel-cr-rrt-henry-tornow.jpg
https://www.oberwesel.de/en/wandern0/stadtmauerrundweg/

Bacharach:
https://upload.wikimedia.org/wikipedia/commons/4/4c/Bacharach_BW_9.JPG
https://upload.wikimedia.org/wikipedia/commons/c/c7/Bacharach_BW_1.JPG
https://c2.staticflickr.com/8/7350/9674920482_e2743ed02b_b.jpg

Russ has the perfect suggestion. Both towns are a delight. You could even stay overnight (??) at Schoenburg Castle in Oberwesel or Hotel Zur Post in Bacharach. And eat the famous Reisling Cheese Soup at Altes Haus - the date on the outside of the half timbered building is 1368.

One year before a flight out of FRA, we stayed in Aschaffenburg and rode the train right into the airport the next morning. The town was lovely.

We arrive at 10am on 5/9 and depart 4pm on 5/10. Thank you for the ideas!

The castle looks incredible. They have availability for our 1 night. Silly question probably, are there taxis that take you up?

If you want to spend time enjoying the towns themselves, clifftop castles becomes somewhat impractical. You can't just drop your bags and head off to explore on foot so easily. I would encourage you to find a place in town. Look into Weinhaus Weiler in Oberwesel. In Bacharach, the Altkölnischer Hof gets good marks. There are other places with charm and good locations as well.

You could also stay a bit closer. Take a look at the lovely town of Eltville? Lots of half-timbered buildings, quaint cobblestone streets, a church built in the 1300's, dry moat planted with 1000's of roses and other flowers, a small rampart to walk, great promenade along the river with no trains to get in your way, and plenty of wine bars and delicious food. It isn't as far from the airport, but you need to switch trains in Wiesbaden.
https://www.rheingau.de/villages/eltville

Thanks everybody! You are a great help.

I have to add Eltville to my "list".

We had a car, so Russ is correct about the castle idea. Are there taxi's ??

The hotels in Bacharach would be nice too because you could find one close to the train station.

Here's what the Washington Post recommends for long layovers in Frankfurt - https://www.washingtonpost.com/lifestyle/travel/frankfurt-on-the-fly-a-long-layover-allows-for-a-walking-tour-of-the-german-city/2017/12/21/ff7c2ce8-de9c-11e7-89e8-edec16379010_story.html