Train
To get to Meissen, you'll take the S1 train from Dresden's main station or Dresden Neustadt station. Trains between Dresden and Meissen leave every 30 minutes until midnight. If you are flying into a different European city, it is still easy to reach Meissen connecting through Dresden. Two airports in the Dresden area are Berlin Brandenburg airport (BER) and Prague's Vaclav Havel airport (PRG). From either of these cities, you can catch an IC (inter-city) train to Dresden and then connect to Meissen.
Hotel
This hotel is located right next to Meissen's Albrechtsburg castle. Be warned it's a hike up the hill, but the views are well worthwhile!
Hotel
The Dorint is located right along the Elbe river with a great view over the river into the old city. Walking into the city is just a 10 minute walk over the bridge. If you'll be travelling by car, the Dorint has easy on-site parking.
Travel Note
Airbnb has a lot of quaint options if you're looking for something more apartment-style or if you're travelling in a bigger group.