We arrive in Frankfurt in Sept around 10:30am and will be renting a car and driving to Munich or Fussen. We want to visit Neuschwanstein Castle the following morning and then visit Munich that evening since the following morning we will be checking out and then touring Dachau on our way to Treir.
We had thought of staying both nts in Munich but then wonder if it would be better to just stay near the castle (any suggestions) the first night since we will be tired plus we could get an early start on the castle trip. Then we could drive to Munich for the rest of the day and evening. Your thoughts and ideas are appreciated.

You can reserve your spot on a tour of Neuschwanstein and Hohenschwangau. The tours are timed to the minute and you have to be there to be on your tour or you lose out. That should help your planning.

There is a lot of stuff to see between Fussen and Munich and a lot to see in Munich if you can spare the time.

You didn't say how long you have to spend in Germany. Since it a few hour's drive from Frankfurt to Munich or Fussen (see ViaMichelin.com) and then more driving hours to Trier you might think about saving part of the itenerary for another trip unless you were wanting to see Germany through the windshield.

I checked and it is 4 hours Frankfurt to Fussen, 3:45 Frankfurt to Munich, 5 hours Munich to Trier. Depending on where you are flying from this may be on the tail end of 15-17 hours of flying.

FYI, if you rent a car in Germany at an Airport or Train Station they add a 19% surcharge on the entire bill. If you can get it from another car lot you can save quite a bit.

We will arrive at 10:30am 9/13 and are thinking about staying the first night near the castle and then the next night, 9/14 in Munich instead of both nights in Munich so that we get an early start on 9/14 to see the castle and then head over to Munich to visit the rest of the day and evening. We see that Hotel Garni Schlossblick is near the castle and do you have any comments on this place since all we need is a place to stay the first night sicne I'm sure we will be tired from the plane flight.

I am not familiar with that hotel, maybe someone else here can give you advice on that. How many of you are there? I assume you are driving. How many days in all will you be in Germany. If you don't already have you tickets you may want to consider flying into Munich to save some driving time.

With the jetlag factor, would it be safer to take the train from Frankfurt to Fussen? Fussen is only 15 mins on public bus to the castle.

I think the castle and Munich in one day sounds like too much, but it's up to you. As AisleSeat stated, you need to visit the castle on a guided tour. If you want to guarantee a morning visit so you can squeeze Munich in in the afternoon, then it would be advisable to reserve your tickets on-line. It costs about 1.90 euro reservation fee, but well worth jumping the queues, especially with your tight schedule.
http://www.hohenschwangau.de/ticketcenter0.0.html

Hi - I stayed at the Hotel Hirsch in Fussen in Sept. Very quaint, sweet little hotel in the little town. I think it was pretty reasonable and very close to the castles. Have fun!