Small bikes (125 step-through type) are no longer rented in some areas due to too many accident prone falang drivers ;-)
"Big" bikes (250cc and rarely above) are easily rented in Vientiane and Luang Prabang, sometimes also in Pakxe. If arranged suffieniently in advance some of the rental companies can drop a bike for you somewhere else, e.g. at Huai Xai (border with Thailand). Both Jimoi and Jules are good guys to rent from. More info on the gt-rider forum.
The GT-Rider map of Laos is pretty much mandatory (the rental places will have it) and the only decent map of the country in existance. As for routes ... too many to write about here. And it depends very much on what you want, paved road or off-road (fantastic in Laos), backpackers, sex/drugs/rocknroll, nature, landscapes, hilltribes, culture ... ?