The Black Forest is a pretty huge area, of roughly 100x30 kms.
I think you will know better what option is best for you if you first compile a list with your potential sights.

They can all be in the Titisee area (which is one of the hotspots), so you will not need a car.
Or scattered all over the Black Forest so you will want to have a car.
The car would also give you the flexibility to hop over to Alsace or Basel if you feel like it (depending on where you will have your base in the Black Forest).

As you already mentioned as one option, if you opted for the car it would be more convinient to take the train south to Baden-Baden, Offenburg or Freiburg and rent a car there. Most bigger stations have rental car locations nearby or on premises.
And the drive from Frankfurt is not only marginally scenic but also one of the most crowded north-south routes thru Central Europe.

You really need to a car to explore the Black Forest - since it is primarily small towns and hilly countryside.

Not sure what you consider affordable. My brother bought a pretty cuckoo clock (a small one) about 15 years ago and paid about $200. I would expect a similar one to be much more now given inflation and the the fall of the $ against the euro.

I probably would pick Trieberg as the center of my stay. Itis quite interesting, especially for someone interested in Kukucks Uhren. It has a K. museum. T. is the center of the Schwarzwald Bahn, a scenic train ride through parts of the Black Forest. From T.the intesting points are all within a half day or full day's drive. Not to be missed is the Freilicht Museum Vogtshof, about 35 km north of T. Other places worth seeing have been mentioined in the other postings.

There are two major north- south routes in Black Forest, the Schwarzwald Hochstrasse (rim road) and the Schwarzwald Taeler Strasse (valley road). Of the two, then Taelerstrasse is the more interesting in terms of unique villages and the region's culture. The former is primari;ly scenery.

I wqould defintely get a a car for flexibilty and access to to places off the beaten path.

You could take the train from FRA to Baden-Baden and pick up the car there. It would save you having to drive the busy Autobahn A-5 right vafetr getting off the plane. The first day cost difference is probably a wash, train compared to car. For the whole stay, train would be cheaper, but you would have to use train and busses to see many of the places.

"I have read there is a free card for Black Forest transportation unless you stay in Feilburg - then I suppose it is not free? Should we rent a car in Frankfurt and drive to have more flexibility over the train?"

I've driven in the BF and also traveled by train, and for a 3-night stay, I really can't think of a reason that you'd need a car. You are correct about the free trains (free buses too) and correct that they aren't free if you stay in Freiburg. But you can stay in about 130 other towns and get the free Konus pass from your hotel or inn:

http://www.blackforest-tourism.com/konus

I suggest that you stay in one strategically-situated town that allows easy access to most of the BF. Gengenbach, a very handsome walled town like Rothenburg, but smaller and without all the tourism, is just about perfect. You can hop on a train there and reach Freiburg in one hour on the regional trains (the ones that are possible with the Konus card.) Much closer at 20 minutes away is Hausach, the destination station for visiting the Vogtsbauernhof open air museum (bus connection or walk from there.)

http://en.vogtsbauernhof.org/

Triberg and Villingen are popular and interesting destinations within an hour of Gengenbach on the same train line as the museum; this is the scenic Black Forest Railway line:

http://www.black-forest-travel.com/places-of-interest/black-forest-railway.html

Schiltach, with maybe the most exceptional collection of half-timbered buildings in the BF, is a tad over 30 minutes from Gengenbach:

http://www.schiltach.de/ceasy/modules/cms/main.php5?setActiveLanguageId=2&cPageId=223

"I would like to see the coo-coo clocks being made and the house sized ones if possible."

Triberg is the cuckoo clock capital of the Black Forest. The Triberg TI office says you can watch production at Hubert Herr's shop; you might contact him to see what hours this is possible:

Hubert Herr
Hauptstr. 8
78098 Triberg/Schwarzwald
Telefon: +49 (0) 7722 4268
Telefax: +49 (0) 7722 5927
eMail: info@HubertHerr.de
http://www.hubertherr.de/english/chronicle.asp

Furtwangen, home of the cuckoo clock museum is a 30-min. bus trip from Triberg; maybe do Triberg and Furtwangen on the same day.

http://www.furtwangen.de/servlet/PB/menu/1265433_l2/index.html

Titisee is a tourist destination on a beautiful lake of the same name; you can get there on the Konus Card too via Freiburg (about 40 min. ride through the "Hells Valley" railway, also quite scenic.)

A car is not needed as long as you don't plan to go anywhere that is not served by train, don't want time flexibility, don't want to explore scenic driving routes and don't enjoy driving.

If visiting larger cities, a car is a liability. When visiting rural and scenic areas, it gives you many more location and time options. The Black Forest is much more the latter.

twosassyk: This page (only in German it seems) shows the many railway lines that cut through the Black Forest; Gengenbach (near Offenburg), Triberg, and Hausach lie on line 4, the Black Forest railway, the most scenic of the routes. You'll find double-decker trains on the BF Railway and other routes, which are great for enjoying the scenery; it's not necessary to dislike driving to enjoy this ride:

http://www.bensbauernhof.com/russschwarzwaldbahn.jpg

Schiltach is on line 10 and like the other towns is served by direct trains from Gengenbach.

You'll find Freiburg and Titisee on line 5, the Hell's Valley route.

Oops - omitted the rail line link:
http://www.schwarzwald.com/karte/bahnlinien.html

FWIW, I found Gengenbach pretty and nice, but not that exceptional. There are plenty of small towns like it. And tourism has grown quite a bit -- it's not an "undiscovered gem" any more. There were tour groups wandering around on my last visit. The Gengenbach tourist booard has ads in many magazines these days; while at the hairdresser's two weeks, I flipped through a variety of German-language lifestyle magazines and saw several "visit Gengenbach" ads. That's no reason not to visit or stay there, but don't expect to be in some secret, tourist-free idyll.

Well I can't seem to get a flight or train from Stockholm to Frankfurt or the Black Forest area that does not take all day long to get there so trying to determine if worth keeping this desired location. We arrive in Stockholm from a cruise at 7 am on Sat 7/14 and all flights connect and take the majority of the day just to get to Frankfurt and are about $400 one way for each of us.

Even if we are willing to pay $800 for two one way tickets from Stockholm to Frankfurt we would still have to take the train to the Black Forest and not sure all of that would be possible in a single day.... And if not would it be worth going to the BF with only 2 nights...?

It seems a tad rude to request advice on the details of a BF visit and cuckoo clocks etc. when you aren't sure you can even get there.

$400???? Did you check Ryanair for Stockholm to Frankfurt Hahn, or Karlsruhe Baden-Baden airports? Probably $100 or less each. But even so... You'll spend most of a day getting to the BF from Stockholm. Might be better to visit the Rhine/Mosel region since Frankfurt Hahn is smack dab in the middle of it.

Russ - I am not rude and trying to get it worked out thanks for your response. I am using Kayak.com using multi city pairs and trying all combinations that I can work out to try and get back to Frankfurt to have the most time at the BF. We have been to the German corner on a previous visit last year. Round trips from / to Stockholm I have gotten it down to $380 (knowing we will not use the return flight) and I continue to change the return flight we will not use trying various dates to get the cost lower if possible.

Tickets with Ryanair are $45 each on 7/18 from Stockholm to Frankfurt Hahn; shuttle buses run from there. You can check the website yourself for your actual travel dates. Ryanair, like many other discount carriers, isn't on KAYAK.

Thank you Russ - I just looked and on Sat 7/14 no flights are returned for Stockholm to Frankfurt Hahn. The search continues