I've never had problems leaving Munich for the US when I arrived 2 hours before flight time. However, if you are flying United, their gate is on the very end of Terminal 2, a pretty long walk. Last trip out, we asked for transportation to the gate for my partner. We had to wait for a wheel chair (no motorized cart), and, by the time they got her to the gate, they were boarding the flight.
If I were doing it, I'd try to get to the airport by 5:15. According to the MVV (Munich metro) website, there is a bus leaving the Freising Bhf at 4:45, getting to the airport at 5:07.
If you stay in Freising, it's a short trip to the airport in the morning but a 40 min trip each way into town. A Partner (up to 5 people) Gesamtnetz (entire metro district) Tageskarte (day ticket) for 21,30 € will cover your round trip S-Bahn to downtown and any transport in town. If a regional train comes into the Freising Bahnhof headed for the Munich Hbf, take it. Regional trains only take about 29 min to the Hbf.
One option would be to come into the Munich Hbf, leave you bags in a locker, take the tour, then go out to Freising. There are things to do in Freising in the evening, like eating dinner and drinking beer at the Weihenstephen brewery on the hill.
I don't think Booking.com will give you a truly broad selection of accommodations near the airport. Freising's website, www.freising.de, has a comprehensive English listing of accommodations (Gastgeber) in town.
Some people on this website used to recommend Zur Gred as a place to stay. For a while you couldn't book directly with them, but their website is back up.