When I backpacked Japan I bought a (kind of big) trolley/backpack which was the coolest thing ever, I bought it at The sports authority for around 70 USD maybe you can find something similar where you are.

I would say that most efficient thing to do is choose a trolley because you know, Japan has designed the country for bicycles (the ramps at the sidewalks, you think they are for disabled? noup, bicycles :P) so you can pretty much roll it everywhere.

But personally I prefer the backpack as I can be looking at the map or doing something with my hands while walking without having to worry about bumping my trolley into something. the thing I hate about them (and may help you decide better) is that it's uncomfortable using it in urban public transportation as you must take it off every time you get in to avoid hitting somebody and the trains are always really crowded to do it or put it on the shelves. Trolleys are easy to control in this case.

I hope my advice helps!