Eurail trip Mittenwald to Basel Switzerland

According to www.bahn.de, going through In.sbruck would save you about half an hour or even less. So it might not be worth the extra expense. On the other hand, the trip through Innsbruck and over the Arlberg pass will be more scenic than the journey via Stuttgart and Karlsruhe.

Olsen, you need to look this up on the DB (German Railways) website: https://www.bahn.com/en/view/index.shtml
This is the place you should be looking up all rail trips in Germany and surrounding countries.
I just did so for a random date in April. The journey takes about 6½ - 7 hours. Some options are via Innsbruck and Zürich, which therefore involves going via Austria and Switzerland, but others go via Munich, so you would stay in Germany. For example:

Mittenwald dep 09:36, München-Pasing arr 11:19
München-Pasing dep 11:36, Stuttgart Hbf arr 13:45
Stuttgart Hbf dep 13:58, Karlsruhe Hbf arr 14:48
Karlsruhe Hbf dep 14:58, Basel Bad Bf arr 16:34

Note, this connection is now selling for €29. How much will your pass cost you per day?

The question you did not ask is will you be covered to Basel, as it is in Switzerland? The answer yes, because "Basel Badischer Bahnhof" is owned and operated by DB (German Railways) and counts as a German station, even though it is on Swiss soil. The other station in Basel ("Basel SBB") is owned and operated by SBB (Swiss Railways), and Swiss fares apply.

You an search any journey you like to find out the routes and the towns along the way at
http://reiseauskunft.bahn.de/bin/query.exe/en

The fastest and most direct journey from Mittenwald to Basel take you through Innsbruck in about 6 hours.
But it's also possible to travel to Basel in 7 hours via Munich and Stuttgart Germany. A rail pass could be used on this route without crossing the Austrian border. Note that advance purchase tickets for this trip can be had from DB for as little as €30-40 each.

I'm not sure what your entire itinerary is or why your itinerary is constructed such that you are traveling from Mittenwald to Basel. If your point is to see Switzerland, then why are you passing straight through without stopiing? Perhaps there's a more convenient order of travel for you that wouldn't necessitate this particular, lengthy journey. I see from your other posts that you'll be in A'dam and Munich for O'fest as well, but that's all I can ferret out. Where else will you be in Germany? One option that comes to mind would be to stay in Augsburg for a few days and do day trips by local train into Munich for O'fest and to Mittenwald. Augsburg-Basel takes only 4.5 hours. Rooms in Augsburg should be cheaper, more available, and less demanding about money transfers 6 months in advance!!

Also, rail passes tend to be overpriced. Europeans travel all over their own continent without them, and often do so more cheaply than we do with our rail passes. Advance-purchase fares like the one above are just one example. If you share your specific travel plans, we might be able to provide some tips that the Euro-folks use.

Thank you all for your suggestions! My entire itenerary is as follows:
Fly into Munich - Bamberg 2 days
Regensberg 2 days
Munich Oktoberfest 1 day
Mittenwald 2 days
Basel 1 day - Pick up our cruise ship the following afternoon

8 day Rhine River cruise covering 4 countries

Ending in Amsterdam where we will spend 2 days before flying out.

Other then the Mittenwald to Basel length of time on train the other trips are not too long.
I've had the pleasure of traveling extensively throughout Germany over the years and one of my enjoyments is traveling by train...and of course the beer! I know the trip can be tweaked, but for us it's very doable. Other then Munich this will be our first visit to all the locations I've chosen. Lastly, I think that purchasing the tickets independently might prove to be a good suggestion as well, I'll research the cost and make my determination.

Thanks to all who contributed their suggestions!

Olsen, from your list, all the rail trips are in Germany (allowing for Basel Bad. Bf. being officially in Germany). So why are you buying a two country pass?
And, since Mittenwald to Basel is the longest leg, and can be had with advance booking for "from" €29, is a pass worth the money?

All of the journeys except the long one are within the state of Bavaria and so all are covered by Bayern-Ticket or cheaper. And that includes local bus and tram which your pass doesn't.

How much are you paying per travel day with the Eurail Pass?

Don't shortchange Basel. If you are staying in a hotel within Basel your local transportation there will be free.

That itinerary clarifies things...

"I think that purchasing the tickets independently might prove to be a good suggestion as well, I'll research the cost and make my determination."
Here are some tips...

On Day 1 you have a 3-hr. train ride to Bamberg after an international overnight flight. I'd be VERY eager to check in somewhere closer. If you can't/don't want to do Munich first, I suggest heading to Regensburg first, only 1.5 hours away (Bayern Ticket day pass, €31/2.)

For Regensburg-Bamberg you can find 2-hr regional train connections (Bayern Ticket, €31/2.)

For Bamberg-Munich it's 3.25 hours on the Bayern ticket (€31/2) using regional trains, or whatever you can find on a pre-purchased saver fare for the high-speed trains (2 hours or so.)

For Munich-Mittenwald, it's 2 hours and €26/2 with the Regio-ticket Werdenfels day pass.

Mittenwald - Basel = saver fare. Book RIGHT when tickets first go on sale to get that €30-€40 price range, and be sure to enter Stuttgart as an intermediate stop (with no stopover time) to ensure you see all the saver fare itineraries that are available for your date.

Buy all the day passes in Germany at the station. Pre-purchase gains you nothing but the chance that you will want a refund for a non-refundable day pass.

When I add all those fares up, I get about €200 total or less for two.

Outstanding! I think there's no doubt I'll be purchasing my tickets independently versus buying a pass, saves money and provides more options.
Regarding passes, I did find out that Eurail is offering one additional day at no cost if you buy them before the end of March. (I.e. 5 day Select pass becomes 6, and so forth)
I appreciate all suggestions and you all made my decision easier. My last request is to anyone who has spent time in Basel. Can you suggest a good location and a moderately priced hotel. Again, I've got about 1 day in Basel to explore it before I catch my ship the following late afternoon.

Much appreciated

If I were traveling Mittenwald to Basel, I would definitely take the much more scenic route through Austrian Alps via Innsbruck.

http://www.seat61.com/international-trains/trains-from-Innsbruck.htm#Innsbruck-Switzerland

For hotels in Basel, go to the official city website, it lists them all plus lots of info on what to see: https://www.basel.com/en
I have never actually stayed in one, as I live here. Prices start at CHF 100 per night for a single room, so expect to pay CHF 150, more if you are unlucky enough to hit a week when a trade fair is on. Makes sure you pick a hotel in Basel City, no problem getting around the city, and you will get free public transport (trams+buses) for the duration of your stay.

I agree with Creek, if you no longer have the restriction of the Rail Pass, them the better route from Mittenwald to Basel is via Innsbruck and Zürich, much more scenic. It may cost more though (German rail is cheaper than Swiss).

Make sure you know where your boat leaves from, there are 3 different places the cruise boats can dock.

I stay at the Ibis Hotel (part of the Accor group) which is very close to the SBB station (out the Media Markt end, downstairs, turn right, at the next corner), on 2 or 3 tram lines with very frequent service all over Basel, a decent breakfast and fair prices.

I haven't stayed at any of the traditional or more central hotels because my wallet would not let me.

It doesn't have to be a choice between through Germany via Stuttgart and Karlsruhe or to Innsbruck and through the Tirol to Zürich.

The route through the Tirol is very scenic, but you miss some of the best parts, around St. Anton, because those parts is all in tunnels. On the other hand, you can also get from Mittenwald to Switzerland via Garmisch-Partenkirchen, then along the Außerfernbahn via Pfronten to Kempten, and from there to Lindau and around the end of Bodensee to Zürich. There will be a short stretch through Austria between Lindau and St. Margrethen, but you can do it for bout 8€ per person, less than adding Austria to you rail pass. That route, although longer, will be far more scenic than via Stuttgart and Karlsruhe.

Lee, that is the shortest but slowest route. What you describe would still require transiting both Austria and Switzerland, but the OP has now I understand been persuaded away from a pass.
But, there is a tweak on your route. It is possible to get from Lindau to Basel solely on DB (German) rails: Lindau, Friedrichshafen, Singen, Schaffhausen, Basel, with only one change in Friedrichshafen. It does dip into Switzerland at Schaffhausen, but it stays on DB tracks and DB fares apply. The whole trip can be done very cheaply on two Länder tickets, Bayern + Baden-Würtemburg.
This route would be the slowest of all the options.

This route would be the slowest of all the options.

Wells, let's make it even slower and nicer:
If there is enough time, you can fit in a short (1 hour) lake cruise at lake Constance by taking the Catamaran ferry from Friedrichshafen to Konstanz and taking from there the train to Basel via Singen.

http://en.der-katamaran.de/

It may cost more though (German rail is cheaper than Swiss).

The cost is pretty much the same. You can buy Innsbruck to Basel saver tickets from ÖBB for €29 each, and then just buy the tickets for Mittenwald to Innsbruck at the station in Mittenwald for €10 each.