Which Way Is Better for a Late Morning flight?

Not sure if you are driving or taking the train. Personally, I'd stay at an airport hotel and take the train or bus over to Freising to stroll around. Or stay in Freising.
We stayed at the Hilton Munich City above the train station and it's about 45 minutes on the train to the airport. If you are getting in later in the day and leaving in the morning, for convenience I wouldn't choose this.

If I have an early morning flight to EWR, I prefer to stay in Gasthof Maisberger in Neufahrn, a very short S-Bahn ride from the airport. The hotel is opposite to the Neufahrn S-Bahn station and offers way more value for your money than any hotel in the center of Munich.

I always opt for a late morning flight, just less hassle. My preference is always to stay in town, have a great meal, maybe an evening drink, a nice stroll, and a good sleep. Munich would be much better than some airport hotel. Good second choices might be Freising, or maybe Erding, not as much action as Munich, but some charm.

Stay anywhere near the S-1 or S-8 SBahn lines, hop on, direct to the airport.

Some potential factors are not specified by OP here, so we kind have to make a guess....

If you are driving in and dropping a rental car off at the airport, then taking the S-Bahn
to stay downtown and then back out to the airport the next day will run you ~$75 for
two people, which may affect your economic evaluation.

If your flight is really early in the morning, then the hotel near the airport is better, but
check the shuttle operating hours and departure times. Sometimes there are fixed
departure times and it does not leave exactly when you are ready. Also, there is
often a charge to go back to the airport.

If you get in late and are just looking for a place to sleep, the towns along the S-Bahn
line will be cheaper and quieter than downtown. Just make sure you know how to get
to the hotel after getting off the S-Bahn.

Assuming you're departing Munich on a weekday, the Hauptbahnhof will probably be
quite busy in the morning, and last year (probably still this year) there is a lot of
construction in the station.

So, unless you really want to go back into downtown Munich, I think staying near the
airport is a better plan. A middle ground option is to take the train from Salzburg to
Ostbahnhof and stay somewhere around there. The train to the airport takes a bit
less time.

Thank you KD, Fritz, Paul & shoeflyer for your replies. I have edited my post to be more specific.

I will check out Gasthof Maisberger. It seems very convenient.

We spent a last night in Germany in Erding, 20 minutes from the airport. Best Western Park Hotel. Nice hotel, charming old town.

Thanks again for all of the advice. I just booked a room at Hotel-Gasthof Maisberger. I like that it is next to the S-Bahn and so close to the airport.

Andrea, you won’t be disappointed. That hotel is a gem. The restaurant is also excellent.