"Day trip to Andechs Monastery"
This trip involves a bus ride as well and takes about an hour each way from Munich. Probably closer to a half-day trip. Don't follow Rick's walking route from Herrsching if you don't enjoy hiking.
"Day trip to Neuschwastein Castle (book a guided tour)"
IMHO...6 nights is too much time in Munich. I would not spend all 6 there just to include a lengthy bus trip like this one to N'stein. (You already had another long bus tour outing to Berchtesgaden, right?) The N'stein tour takes just 30 minutes and is probably not worth the time and expense if that's your only objective. (Also - be sure to ask about how much WALKING you will have to do on such a tour. I suspect it's still a lot.) But... if you STAY a night in Füssen instead of day-tripping, you will have a better opportunity to enjoy yourselves more fully in a more relaxed way in this very attractive place. And you could get there and back using inexpensive public transport like the Bayern Ticket.
Some Füssen town highlights.
"Do you suggest staying at Koblenz or any other area to best explore this region and visit these 2 sites?"
I almost never suggest staying in Koblenz. The atmosphere in smaller town like Boppard (which Sam suggested) is much better, and your river cruise is much easier to do as well; just take the train to Bingen, and the cruise back to Boppard. You can step off the train on your way to Bingen in St. Goar (Rheinfels Castle) or in the towns of Oberwesel or Bacharach for sightseeing - then take an afternoon boat (14:30 or 16:30) back to Boppard.
And instead of Burg Eltz, consider visiting these castles, all of which are easier to reach:
Marksburg (across the river from Boppard and north in the town of Braubach.)
Rheinfels (St. Goar.)
Reichsburg (Cochem) on the Mosel River:
Do you plan to visit Trier? It's a very worthwhile destination on the Mosel River. If so, I suggest that you split your time - 2 nights in Boppard (Rhine,) 2 nights in Cochem (Mosel.) Trier is a long day trip from the Rhine towns. Or better yet, 2 nights / 3 nights if you can steal a night or two from Munich.
"Fly Back from FRANKFURT airport on 17th April (Friday) morning"
Make sure that your last night is spent closer to FRA if you must leave in the morning! Mainz is a good place - 25 minutes from the airport. From Boppard it will take you a minimum of 1.25 hours (direct train) or closer to two hours (connecting trains.) Of course you will probably need to be at the airport 2.5+ hours prior to your flight. So maybe if you have a late morning flight, like 11 am, you could leave Boppard at around 7 am. But that's pretty early for most people and makes for a very long travel day.