Base for Rhine/Mosel Visit

Have you considered Boppard? A charming river town with a nice buzz, many restaurants , and easy access to transportation.
Russ is the resident expert here on the Rhine area, perhaps you can find him , and his many detailed and helpful posts. We were there May 2022, and really enjoyed the area.
Have a great trip.

I found Koblenz to be perfectly charming, with lots of lovely turn of the century buildings and some beautiful old churches. Plenty of restaurants and the view of the fortress is wonderful. The gondola ride up there is stunning. Koblenz has a lot to offer, besides just its' central location.
https://www.visit-koblenz.de/en/sights-attractions

https://community.ricksteves.com/travel-forum/germany/help-with-itinerary-mid-april-2024-frankfurt-to-munich

The above Search may be helpful. Safe travels!

I used Koblenz as a base once and it was fine as it proved central for my cycling on the Mosel, Lahn and Rhine.. Having a car makes its centrality less important, I think. You might also look at some of the towns along the Rhine ( I like Bacharach ) and find an apartment that suits you.

I've stayed many nights on both rivers and spent a fair amount of time in Koblenz and honestly, it does very little for me. It's just OK... it's a mostly modern city, a shopping mecca for the area, one that can be a good choice for the Rhine/Mosel in the winter months on account of its being a train hub for outings on both rivers. But the charm on both rivers is better found in the smaller places. I'm a dedicated train traveler whenever I'm in Germany, and although I'm perfectly able to reach any of the river towns easily by public transport, the smaller towns tend to be way too quiet for me during the winter... hibernation is not my thing. So I have stayed in Koblenz at that time of year, but in spring, when all the smaller, more charming towns in more attractive surroundings have already opened their doors and shutters, I would never choose to book in Koblenz.

CAR/TRAIN: A car is advantageous, IMHO, only if you are planning to stay in REMOTE towns that are not on the railways or near the river, or in otherwise difficult locations. For example... People that stay in Oberwesel at the Auf Schönburg Castle-Hotel probably aren't so interested in climbing and descending the steep cliffs on foot - or calling a taxi - every time they want to head out for a meal or a glass of wine or something. When I've stayed previously in Oberwesel - and in Bingen, Bacharach, St. Goar, and Boppard, all of which are on the same riverbank - I've found a room in town, then taken a short, mostly-flat walk to the rail station for outings to other towns. All the river towns are built on narrow, flat spits of land near the water, and they're small, so by rail and foot it's all rather simple. Same if you are visiting wineries. Some people reason that they will have to travel out to the vineyards to taste wine, but the wineries are typically right in town. This winery in Boppard, for example, is just a few steps from the river, the town center, and the train station:

https://media-cdn.holidaycheck.com/w_1280,h_720,c_fill,q_80/ugc/images/95a51094-9ca5-3a93-8dba-6c9093acacf3

And obviously, you can be a lot freer with your winetasting if you aren't having to climb behind the wheel.

Cochem is a beautiful town on the Mosel. I always stay right in the old town zone there. On Tripadvisor, the top 5 listed wineries are right in town - you won't be driving to these places in any case - just click on "Map" at the page below to find them:

https://www.tripadvisor.com/Attractions-g198637-Activities-c36-t132-Cochem_Rhineland_Palatinate.html

Maybe you should consider staying with a winemaker somewhere... I know the Haxel Winery in Cochem has rooms.

Boppard is a good smaller base town with nice riverfront hotels and numerous restaurants; it's 15 minutes south Koblenz by direct train, and they offer a free rail pass for local train travel (Guest Ticket.)

By car, Koblenz isn't necessarily a time saver...

Koblenz > Cochem = 45 min's
Boppard > Cochem = 45 min's

By train, Koblenz > Cochem can be done in 37-38 min's.

I think you'd be wise to carve out at most 8-9 days for the Rhine and Mosel. See some other places for the rest of your time. If you want to DRIVE, then you might choose to pick up a car in Koblenz AFTER your stay. There are places with castles, charming old-world towns, wineries, etc. for which a car can be more handy. Monschau springs to mind. The Odenwald and the Pfalz areas might interest you. Check out the themed driving routes as well...

German Fairytale Road
German Half-Timbered-House Road

Another option for stay on the Rhine and not far from Mosel river Valley is the Ferienhof Hardthöhe above Oberwesel with views from the Chalets to the by Russ mentioned Schönburg Castle and the Rhine

https://www.ferienhof-hardthoehe.de/

Rhine below your feet
Mosel in 50km
Koblenz in 40 km
Rüdesheim in 30 km

Chalets and Houses are a bit expensive you can book them with breakfast and Diner buffet

If you do plan to visit wineries and drive, the laws in Germany about drinking and driving are pretty severe. I'd plan on not driving after winery stops. Either train/bus approaches to travel, or visiting wineries without the need for a car, seem like better options.

I'm sure Koblenz has changed since our 2011 visit (for a 1-time flower/garden show). But we could not find enough choice of attractive, comfortable accomodations. Because we did not want to have a car in a city, we stayed in a family-owned hotel in Andernach, Alte Kanzlei. I'm NOT recommending that for you, but I should say that their private parking, off-street, was a selling point. In fact, we took the train for our multiple visits to the BUGA show in Koblenz. It was nice to eat outdoors in the Andernach's small historic square, and not hear much English spoken.

I'm a little prejudiced against Koblenz because of pro-business, disingenuous decisions about that cable car. Because it's in the middle of a UNESCO WHS, the cable car was promoted as a traffic-draw during that flower show, to be demolished within two years. Of course, like the Delacorte Theater in Central Park, it became, somehow, a "permanent temporary structure!"

We then moved to a luxury boutique hotel in Mulheim, Weinromantik Hotel Richtershof. It was an enjoyable location for drives to Trier and around the Mosel. Although the Mosel is attractive terrain, I found the "river" less interesting and less navigable than the busy Rhine, with fewer "landmarks" (I mean like castles.) Apparently there's a lovely forest walk from the train station to Burg Eltz, but we enjoyed the convenience of the car. Consider a train to wine towns, so you can taste plenty. Note that first-class wineries absolutely require appointments. Bicycles are very big on the Mosel. I consider Bernkastel-Kues too touristy, but it probably has a huge number of accomodations, at every price level. Traben-Trarbach was one of our favorite visits, and on a public-access vineyard walkway/trail, we saw a winery that had accomodations. Don't remember the name.

I'm also prejudiced against AirBnb because it is so harmful to local housing economies. There's a long German tradition of "Zimmer Frei", but clearly that's not acceptable to you.

Thanks to all for the information, especially Russ for all the detail. We look forward to our visit.