To give you an idea of how big (or more accurately how small) the region of Alsace is...
You can drive from Wissembourg (the very top) to Basel, Switzerland (near the very bottom) in about 3 to 4 hours...
And that's mostly on highways.
So flying to Strasbourg will not make any huge changes in your travel times because Alsace is a very small region.
How to Get to and from Your Strasbourg Flight
Strasbourg Airport Shuttle Bus to the Train Station
The Strasbourg airport has a train station at the airport!
Well, it's less than a ten minute walk from the airport. You
can catch the train about 3 to 4 times an hour during the
week Monday through Friday and about 2 to 3 times per hour on Saturdays. It varies.
generally run between the hours of 6am and 10pm. The hours on the
weekends and holidays are shorter than during the week as you would
expect in France.
It's only about 9-15 minutes to the train station in Strasbourg.
There are quite a few hotels in Strasbourg
that are easily reachable from the main train station and you can
usually take one of the trams a short distance to many other hotels and
Taxis are generally available from 6am to 11pm or as long as there are flights arriving.
if you somehow manage to arrive after the last train has left,
you'll very likely still be able to get a taxi or
your hotel if you prefer.
More Information on Air Travel to Alsace
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