Need Basel directions from Basel SBB to Hotel Gas-und Kulturhaus der Teufelhof

Direction 1 -- Exist airport and look left or right for taxi starter/line.
Direction 2 -- Get in Taxi, hand driver a card with address of hotel.
Direction 3 -- Pay driver, get out of taxi, walk into hotel

Given all of the conditions stated in your question, a taxi is probably your best solution. Do you really want to go through two tram changes, and a 20 min walk hauling luggage? There is a time to save money and a time to spent for convenience and comfort.

As you mention Basel SBB, I assume you are flying into Zürich (no flights from the "west coast" to Basel), and getting the train to Basel.
In that circumstance, no way get a taxi from Zürich airport. That would cost you hundreds!

If you are flying into Basel (changing planes somewhere), then the question is wrong, getting to your hotel from Basel airport is a different question. If this is the case please come back and say so.
With hindsight, a direct flight to Zürich (if possible), then the train is the quickest and most comfortable option).

The Teufelhof is a somewhat upmarket hotel. Website: https://www.teufelhof.com/
It is on the edge of the old city centre. The street behind it (Heuberg) is one of Basel's jewels. Click here for photo, the Teufelhof is on the right, just past the one way street sign.

You could get a taxi from Basel SBB. This will cost around CHF 30, still expensive.
Basel is totally a tram city. You cannot drive in the centre. A tram ticket costs CHF 3.80. Once you check into your hotel you will be given a free transport pass for the duration of your stay.

Directions from Basel SBB to Teufelhof by tram.

1) Walk out the front of the station (not out the back).
2) Buy a ticket (green ticket machine, 1 zone, CHF 3.80 per person)
3) You want a tram 8, 10 or 11 towards Aeschenplatz. It is from one of the two platforms on the right, Easiest to ask someone which tram this.
4) Get off after 1 stop (Aeschenplatz).
5) Ask someone where to find tram 3 towards Musik Akademie (it is 50 metres in front of where your tram stops)
6) Get of at the 3rd stop Musik-Akademie
7) Carry on walking in the direction the tram is going. The Teufelhof is 50 metres ahead on your right. Click here for map

Map of the Basel tram network: https://www.bvb.ch/wp-content/bvb/Dokumente/Liniennetzplan/2019/TNW_Liniennetz2019.pdf

P.S. When they say "20 minute walk", that is from the station if you choose not to take a tram. It is down then up again.

Click here for directions from Basel SBB to Teufelhof on foot. This map says 1,1 Km, 14 minutes.

Chris,
That is perfect!
Yes, we are flying SFO to Zurich, from Zurich airport via train to Basel.
Your directions are very concrete and functional.
We are so looking forward to exploring your beautiful city. I hope the ferries are running; I've read that winter can limit their running.
Thanks again and safe travels!

Chris,
I believe with the Swiss Travel Pass the trams should be free; if not, I read that having a hotel reservation will cover us for the trams to the hotel [not that it is very expensive.]

Thanks again!

Pat, If you have a Swiss Travel Pass it covers all public transport, including Basel trams and buses. So no need to buy tram tickets from the station.
If you have a day in Basel while you are staying there, you would waste a day if your Swiss Pass covers you, as you are also covered by the city pass from the hotel.

Neither pass covers the Basel Rhine ferries. But they only cost CHF 1.60. They run in the winter, theyjust stop earlier when it gets dark.

Chris, we were hoping to use the museum portions of the Travel Pass on the day we stay in Basel. There is a $14 difference between a three-day flexible pass and a four-day consecutive pass, [if I'm reading the site correctly.] Thanks again for all of your invaluable help.

Pat, Swiss Pass prices are here: https://www.sbb.ch/en/leisure-holidays/travel-in-switzerland/international-guests/swiss-travel-pass.html
They are priced in Franks, not $. Below are prices for 2nd class

Consecutive day passes:
Swiss Travel Pass 3 days CHF 232
Swiss Travel Pass 4 days CHF 281
Swiss Travel Pass 8 days CHF 418
Swiss Travel Pass 15 days CHF 513

"Flexi" passes (non-consecutive days):
Swiss Travel Pass Flex 3 days in 1 month CHF 267
Swiss Travel Pass Flex 4 days in 1 month CHF 323
Swiss Travel Pass Flex 8 days in 1 month CHF 467
Swiss Travel Pass Flex 15 days in 1 month CHF 563

Yes, a 4-day non-flexi is only CHF 14 more than a 3-day flexi.

And, one more advantage, the non-flexi passes you can buy on the above website
before you leave home (self-print tickets). The flexi passes you have to buy as physical tickets (e.g. at Zürich airport station).

Chris, we are here and your directions were so helpful. Thanks for taking the time for such detailed explanations for finding the right trams. We love your city and the ease of public transportation. The four- day consecutive Swiss Travel Pass is serving us well- no standing in lines to buy tickets, no planning ahead which train to take, loved the boat ride to Mt. Rigi, and the paper museum- and, of course, the Gluhwein is addictive! Thx so much!

Pat, I'm so glad you are enjoying your trip!

I've been gently trying to get people on here to give Basel a go - I love it there. I've walked past the paper museum several times because I love the setting, but I've never gone in. What's inside?

I'm glad you found your way. What did you think of the trams?

I also really love the boats out of Luzern. I've never ridden one this late in the year. Was it cold on the deck or did you hide inside?

The Christmas opened in Friday, I hope you are going to see it. Two parts, one in Barfüsserplatz, the other in Münsterplatz (where the cathedral is).
The walk down from your hotel to Barfüsserplatz is nice, all pedestrianised old streets. Go out the back of your hotel, turn right.
Past the Rhinoceros (see Google street view if you don't believe me): https://goo.gl/maps/tCdL8wKDsyCxeBUJ9
And left down the stepped street: https://goo.gl/maps/JEnNnEDPmi5NXjaG7
And follow your nose downhill.

Nigel, the trams are great- run frequently, quietly , are clean, and comfortable .

The boat on Luzern was delightful- it was cold outside on the boat, but sitting on the protected rear was better.. From the inside, the windows are kept very clean, ( so Swiss), so you can enjoy the scenery, and the hills are still green. The day we went was cloudy but calm, no wind, the water very smooth. We were so lucky- it was a cloudy day, but the top of Rigi was spectacular: sunny, no wind, as we were above the clouds. A collective gasp went thru the cogwheel as we broke thru the clouds .

Our weather prediction was rain, rain, rain for our days in Basel , Bern, and Luzern, but in actuality we only had a few intermittent showers.

The paper museum is a hands-on experience, which was cool. We were almost the only ones there .

Chris, in Basel , we did get to ride the small ferries that use only the current to cross the Rhine.

The Xmas markets in Bern were also great, and the one closest to the train station was spectacular .

Chris, we did find the Rhino on the way out. Thanks again!

Thanks for the information about the paper museum...