Rail Pass vs Individual Tickets: Which would be cheaper?

Look into using Regional day tickets in Germany. Cologne use Nord Rhein Westfalen ticket, unlimited travel on local trains from 9 am to 3 am next day for 27 Euro. In Bavaria, it's 22 Euro. If there is more than one of you it's an even better deal with a small adder for more than one person traveling together. http://www.bahn.com/i/view/USA/en/prices/germany/laender-ticket.shtml Renting a car for a few days in the Black Forest may be beneficial to see more out of the way places.
You probably will not be traveling every single day, there's lots to see in Cologne and Munich and Paris without leaving town.

Hi, Aaron. Your base-town-with-daytrips strategy is well-suited for the use of inexpensive regional and local daypasses. Individual tickets can then be used to get you between your base towns (Cologne - Nuremberg - Paris - Brussels.) Once you get some costs on this plan, you can compare with railpass options. You will probably want to look into different base towns than the ones you've chosen. To advise you best, we'll need some more info. "cologne as a base for exploring the Rhine-land area for 3 or 4 days" Cologne is not a good base for exploring the "Romantic Rhine" (Middle Rhine Valley) because of the distance and its location outside of the Rheinland-Pfalz travel zone. What daytrip destinations do you have planned, exactly? "Nuremberg to use as a base for exploring Bavaria for 4 or 5 days" N'berg is a great base for northern Bavaria - but again not sure what destinations you have in mind. "Baden-Baden for exploring the Black Forest/Baden-Wurtemberg area for 3 or 4 days" B-B is a lousy base because you have to catch a bus to reach the train station, which lies well outside of town. What BF destinations do you have in mind? It is possible to get a guest card that allows FREE use of all trains and buses for the duration of your stay if you choose certain other towns - there are about 140 such towns - but not in Baden-Baden. Are you traveling alone? Do you have exact or approximate travel dates for the longer trips? That info would be helpful as well.

I'll be travelling alone. The dates so far are influx until I decide which of the areas I want to see more of. "Cologne is not a good base for exploring the "Romantic Rhine" (Middle Rhine Valley) because of the distance and its location outside of the Rheinland-Pfalz travel zone. What daytrip destinations do you have planned, exactly?" Well maybe not the entire Rhine region as I am not sure if it would have that much in the way of medieval history and monastic breweries like it would in Bavaria and the Black Forest. "N'berg is a great base for northern Bavaria - but again not sure what destinations you have in mind." Maybe I'll just split it up between Nuremberg and Fussen. I would stay in Munich but the prices of hostels in late September are pretty high . "B-B is a lousy base because you have to catch a bus to reach the train station, which lies well outside of town. What BF destinations do you have in mind? It is possible to get a guest card that allows FREE use of all trains and buses for the duration of your stay if you choose certain other towns - there are about 140 such towns - but not in Baden-Baden." Would Stuttgart be a better base? What about Freiburg?

"maybe not the entire Rhine region as I am not sure if it would have that much in the way of medieval history..." Medieval history? Base yourself not in Cologne but in the Middle Rhine Valley. It's full of 800-1,000-year-old castles. There are castles (Burg Eltz, Reichsburg) on the Mosel river that you can tour as well. There are medieval festivals and knights' tournaments in the summer months if you time it right. Catch the FALCONRY SHOW at Reichsburg Castle in Cochem. You can book a bed in a castle inexpensively in the towns of Bacharach and Diez. And your daytrips will be 22€/day for nearly unlimited train travel with the Rheinland-Pfalz ticket (daypass) described HERE. Nuremberg: Daytrips by train from N'berg to Bamberg and Rothenburg - both well-preserved old towns - will cost you only 16.80€/day with the Tagesticket Plus daypass.

(cont.)Stuttgart and Freiburg are fairly expensive and lie well outside the BF. Gengenbach is excellent. It offers the Konus card for free travel and daytrips by train from there to Freiburg, Baden-Baden, Triberg, and Schiltach are easily done. Or go deeper along the railway into the mountains to Gutach, Hausach, Haslach, or Schiltach. You'll find the Konus card and inexpensive B&Bs in these places like Pension Zellershof in Schiltach. See Bavaria Ben's review. 18€ is the price per person for a double with breakfast - you'll probably pay a small surcharge for a single if available. HERE is a list of all the towns, including the ones I've mentioned, that offer the Konus guest card, which you get from your hosts and which offers other discounts too. Note that Kirchzarten is a Konus town that lies very near Freiburg if you needed to be close for some reason; it would give you good rail access to the southern Black Forest rail line (Hells Valley line) where hiking is popular - but it puts you a bit farther from the more central Black Forest Railway towns.

If you decide to stay in the Middle Rhine area, you can get a 3 day VRM pass for 36 Euro. It covers all trains and buses it the VRM district that is basically from just south of Bonn to just north of Bingen along the Rhine, up the Mosel as far as Bullay, and the East bank of the Rhine for about 30 km in. You should be able to find lodging in B&B along the Mosel for about 50 Euro/nt.
http://www.vrminfo.de/en/tickets-and-fares/ticket-offers/leisure-ticket/#c421

The 3-day VRM pass Sam mentions is a good deal and may work for you, Aaron, depending on your destinations. However - be aware that it does NOT include Bacharach or points south of there like Bingen, both of which are important towns for most visitors to the Rhine.

Yes, you'd need to spend an extra 8.40 for a round trip from Oberwesel to Bingen, or see them on your way to Nuremberg.