Saxon Switzerland day trip from Dresden

The region is absolutely beautiful. You have names of the cities you could visit by public bus. You can go online and see what bus connections will get you there. We have relatives that were from Dresden, but left in 1939.
I've found any mountains to be best traveled by automobile. That gives you the option to stop as you please as you go along.

The German part is incredibly simple to do on your own by S-Bahn train - that's all I did. Can't help you with the rest. I assume it's not practical do it all in one day by public transportation on your own, if you really want to do all of those things. I'd probably check Rome2Rio to see.

One thought as I took the train back and forth was how pretty the view along the Elbe was (which you can see from the train) and how it might be fun to take a boat in one direction from Dresden to get there.

Before a lot of people invest time: What price is the tour? I guess it is done by bus or van? For a whole day including guide, lunch, transportation, fees, etc. 300-400 EUR will be a fair price. And outsourcing your itinerary and calculation work to a forum ... Ask yourself how much of your private time is it worth to do all that research and booking that stuff.

Some answers you might find here: https://www.saechsische-schweiz.de/en/

If you want to do the same tour on your own you need a car, and it would be a long day.
If you use public transport you can do either the German or the Czech side. This is quite simple. In case of the Bastei area your day would look like this (here is a map):

1. take the S1, a commuter train, to Rathen
2. take the ferry to the other side of the river
3. follow the signs into the Amselgrund (blackbird gorge) to the Amselfall (blackbird falls) and the Amsellfallbaude (a hut). Grab a Wurst.
4. walk a few metres back and turn right into the Schwedenlöcher (Swedish holes)
5. up on the plateau turn left to the Bastei
6. Bastei
7. at the end of the Bastei follow the path down into Rathen again
8. time for coffee and cake
9. cross the river and take the S1 back to Dresden

Re Martin's route - the walk up to the Bastei from Rathen has a big vertical increase with sections of stairways. It wasn't frightening at all for me walking downwards (and I'm scared of heights) but would be very strenuous going up. An alternative if you are less energetic is to get off the train at Pirna and get local bus 237 directly to the Bastei (there is no direct public transport service from Rathen). The buses aren't hugely frequent so check times here by typing 237 in the "linie" box and downloading the resulting pdf. Note that the current timetable is the off-season one, more buses serve the Bastei in higher season. The departure time you want is from Pirna ZOB - ZOB is the standard German abbreviation for "central bus station" which is adjacent to the railway station.

OK, here's my itinerary for the German side of Saxon Switzerland by public transport, without the uphill climb. It's a bit faster-paced as well. If you are more into serious country walking than I am you might want to explore the country on foot more. You can use a regional transport pass for most of the day.

1. Train from Dresden to Pirna.
2. Bus 237 from Pirna to the Bastei.
3. Explore the Bastei, walk down the hill (well-signposted) to Rathen.
4. Cross the river by ferry from the tourist bit of Rathen to the railway station (the ferry does NOT accept local transport passes, make sure you have some euros in small change to pay), take the train to Bad Schandau.
5. Take the ferry from Bad Schandau station to the traditional town centre - this ferry DOES accept local transport passes, or did two years ago.
6. Take a ride on the Kirnitzschtalbahn, a very rare survival of the German rural tramway, which still uses old East German four-wheel cars, to the Lichtenhainer Waterfall, a local beauty spot and back.
7. Take the train back to Dresden. If you still have some time, get off again at Pirna and this time explore the old town centre around the marketplace and church, which isn't spectacular but is fairly pretty.

Many thanks for the helpful replies, especially Martin and Philip for your detailed itinerary suggestions.

Now I just have to choose between going on an organized tour versus a do-it-yourself adventure. I'm leaning toward do-it-yourself so I can pick a nice weather day, but I have time to decide. I'll let you know what I end up doing.

Thanks again!

Although the Bastei Bridge is in a beautiful setting and gets you up close to the unusual rock outcroppings of the Sächsische Schweiz, I didn't feel it was worth the effort to get there. I preferred the Festung Königstein. Königstein is an unimaginably impregnable fortress on a flat-topped mountain overlooking the Elbe above the town of the same name.

From the town of Königstein, which is a stop on the S-Bahn out of Dresden, it's about a 1 mile hike to the fortress, or you can take bus 241 from town to the visitor center. When I was there, a tractor pulled trolley took you the last 3/8 miles from the visitor center up to the fortress if you didn't want to walk it.

The one-way full fare between Dresden and the fortress, including the train and bus, is 6,50€. For 2 people, RT, use a 20€ Familientageskarte.

Once at the fortress, you can rent an audio guide for a few euro, and it explains what all the building are as you walk around the fortress.

It's also possible to do both the Bastei and Königstein fortress on the same day. Train/S1 to Pirna, bus to the Bastei, down to Rathen, ferry, S1 to Königstein, bus to the fortress. Or the other way around, since the Bastei is much more enjoyable after the crowds have left.

Please note that each of the stops listed in the guided tour description involves some hiking. There is no "transferring" from Pravcicka Brana to the Kamenice Gorge by car or bus all the way.

As for the suggestion above taking the tram from Bad Schandau to Lichtenhainer Wasserfall (waterfall), it would be a waste not to hike up to the Kuhstall sandstone arch once you are in the area. Adds about 45 minutes up, a half hour up there, 30 minutes down. And the waterfall is really tiny, you will laugh your ... off!