I guess any bike is fine for a ride -- even RTW -- but I can speak a little about the R3.
I bought a new Rocket III Touring in 2009 and have put 40k miles on it since. I've ridden it all over the US (several times), Canada and Mexico. It's a comfortable enough for long-distance travel but HEAVY. Two-up riding is OK, but there are better touring and 2-up bikes out there.
Mileage isn't great but there's plenty of power.
There were and are some mechanical issues that have plagued the bike; worse, Triumph has refused to acknowledge and address them.
There are at least two really good owners sites where you can get first-hand info from guys just like me---all the pros and cons.
I love the bike but must say there are plenty of other bikes that may be better suited for travel.
I hope this helps.
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