They actually show the same
MVMCP parade in the afternoon the entire week of Christmas at MK. I prefer seeing it in the daytime anyway since pictures are so much better.
Over at the Galaxy Theatre near Buzz Lightyear's Space Ranger Spin they have Mickey's Twas the Night Before Christmas showing. I thought it was cute when we saw it two years ago (although DH and DS were less than impressed) and plan on going to it again this year.
Absolutely everything is still decked out in holiday dress--the swags going across Main Street are gorgeous--wait 'til you see them.
Over at MGM the Osbourne Family Lights will be up each night. There is Christmas music playing, "snow" falling (same soap suds you would have seen at MVMCP if you'd have been there

) and millions of lights. Definitely plan on seeing it one evening.
Each of the parades at AK and MGM also have festive overlays and holiday music, so you won't miss any of that either.
Since this is your first time at WDW during the holidays, I'd also recommend you try to book a package for the Candlelight Processional at Epcot. There is a huge choir singing Christmas songs and a guest celebrity narrator who reads the Christmas story from the Bible. You'll be guaranteed a seat if you get a ticket through the Candlelight Processional deal--dinner and the show. Two years ago we had dinner at the Garden Grill with the characters for our DS and really enjoyed it.
Regardless, you're going to have a fantastic time. Be prepared for the crowds, but know that the weather will be SO MUCH more comfortable than your normal June trips that you won't mind waiting as much.
We'll see you there!