What time of year? That makes a big difference. December to March is usually the ski season. Some resort towns have groomed winter walking trails, but most do not. Late October to early Decemeber and April to early June (varies from year to year) are the shoulder seaons when it's generally too wet and cool to hike, but not cold enough yet for skiing. Most of the tourist infrastructure in the mountains usually goes on hiatus during this time. Late June to early October is the usual summer hiking season, with the single best month usually being September. I would not plan an Alps-centered trip during the shoulder seasons. Too low yield for your money and time.
In general, especially if your trip will occur at a time with less consistent weather, buget at least three nights for each Alpine location. If you only give yourself one full day, you risk having that day becoming nothing more than a foggy rain-out. Adding an extra day gives you a better chance of catching at least some of those views that you traveled so far to see. Since the castles are the main attraction in Füssen, though, and your enjoyment of these are far less weather-dependent, I think you can safely give yourself a single full day here. Lech am Arlberg is abosultely stunning, but I would add an extra night, for the same reason.
"We land in and fly back from Munich. We plan on driving down the Romantic road in a day" A couple of points here. One, the Romantic Road is significantly to the west of the Munich airport, and this would be a very indirect route to reach Füssen. Two, the intention of the road is to link together a series of attractive towns, not that the road itself is more scenic than any others in the area. There's nothing really special that you wouldn't see taking the most direct route from the airport. Three, think about the effects of jet lag on your ability to drive. Some people claim that jet lag doesn't affect them, but when they've done experiments on aircraft pilots to test higher level executive functions (like driving a car), their performances and reaction times were little better than that of someone who is legally drunk, no matter how tired they reported feeling. Especially if you've never driven in Europe before, I would spend your first night somewhere in the vicinity before driving a long distance. Since this is your honeymoon, may I suggest the fabulous Therme Erding? They're about to open an on-site hotel. Or if you want to treat the new wifey to a night of luxury, you can't do better than Munich's Hotel Bayerischer Hof (although you could easily do much cheaper!). You can easily reach Munich by train, and after a night of adequate sleep, grab a rental car at the Hauptbahnhof.
I don't think you have time to fit Vienna unless you drop Salzburgerland or Füssen and Lech am Arlberg. Vienna is lovely, but for nature lovers... well, it's a huge city.
Between Füssen and Lindau, plan to make at least a short stop-over at beautiful Lindau on the Bodensee, epsecially if you have a clear day with an unobstructed view of the Alps. Try to time it to coincide with lunch.
Finally, just realize you'll need to purchase a vignette sticker to drive the rental car on the Austrian Autobahn network. If you approach the border on the Autobahn by Bregenz, there's a border station where you can purchase the vignette. I can't remember if there's a border station on A8 (the Autobahn that connects Munich to Salzburg), but if not, you can buy the sticker at petrol stations near the border.
