It is not possible to get around Lichtenstein by air. Zürich Airport is the closest international airport.
Bicycling through the whole country in a few hours is viable and a great option; roads are in excellent condition and bike lanes are common. For bicycle hire, try the Swiss train stations in Buchs or Sargans, or for an e-bike, the tourist office in Vaduz.
Another option is to grab a free orange rental bike from FreeVeloPoint at one of the 15 stands around the country. There are explanations in English at these points; you'll need a mobile phone to receive the lock code. In Vaduz, the FreeVeloPoint is at the post office.
It's not possible to get around Liechtenstein by boat.
LIEmobil buses (www.liemobil.li) traverse the country and are extremely efficient and reasonable. Single fares (buy tickets on the bus) are Sfr3/4/6 for one/two/three zones, while a daily bus pass costs Sfr5/7/10 for the same number of zones. Swiss Travel Passes are valid on all main routes. Timetables are posted at stops.
Car & Motorcycle
As Liechtenstein is only a tiny country and the roads are excellent, it's easy to get around by car and motorcycle.
The Austrian rail company ÖBB runs a limited service from Buchs (Switzerland) to Feldkirch (Austria), with some trains stopping at Schaan in Liechstenstein. This is not a convenient way to get around Liechtenstein, however.