What is the best day-trip destination to the Wadden Islands? Thank you.

Where are you based? Texel is the easiest island to get to, you can get there by train and ferry from Amsterdam, and make a (long)day trip of it. take the train to Den Helder then the 33 bus to the ferry terminal. You can find out more at http://vvv.texel.net/&lng=en

Otherwise Terschelling is doable as a day trip if you get the fast ferry. You have to get to Harlingen for that though which is a bit of a trek by train (3 hours). So you would be better off staying either in Harlingen or a night on Terschelling.
For info on the ferries to Terschelling: http://www.rederij-doeksen.nl/index.php?nLid=2

I am off to Vlieland for a long weekend on the 6th March!

We will be based in Amsterdam.

Is the Wadden a good choice for a Monday day trip? I ask because it seems as if many museums are closed Mondays.

No, museums are NOT closed on Monday. Rijksmuseum, van Gogh, Ann Frank etc. are all open. Check their websites.

As Ida says lots of museums are open on Mondays.
If you want to do a day trip from Amsterdam, then Texel is definitely the only island which is doable. Maybe you should see what the weather is like - if the forecast is good for the next day then go to Texel. You don't need to book for the ferry.
If the weather is not so good then do something else.
You could hire bikes on Texel to get around, or take the bus.