The last time we've been in the Sächsische, we've chosed the following route:
Train to Bad Schandau, ferry to the other bank of the Elbe, Kirnitztalbahn
to Lichtenhainer Wasserfall
, and then a walk back to the Elbe passing the Schrammsteine
On my last visit to Dresden, I stayed here: http://www.pension-am-businesspark.com/
nice and cosy and friendly staff, but I do not know if they speak English.
One place that is worth visiting: the historic silver ore mine
in Freiberg in Sachsen, 1 h from Dresden by train, but unfortenately it's neither in Dresden nor in the Sächsische...
Something to do at Leipzig: If the Thomaner choir is performing: Motette in the Thomaskirche, friday evening ( 6 pm ?). As far as I know they announce who is performing in the Motette. (It's not a concert but a religious service with music!)
I liked the Leizig zoo (especially the great apes) and I was impressed by the Panometer
with the rain forest exhibition
I stayed here several times: http://www.grandcity-hotel-leipzig-zentrum.de
The hotel is located in one of the typical GDR Plattenbauten
, is in walking distance from the city center. The rooms are rebuilt flats, every room has a small kitchen facility, several "rooms" are former 2 room flats and have a living room, a bedroom and a small kitchen.
A nice place to eat is the Bayerische Bahnhof but there are lots of nice restaurants in Leipzig city center.