Not sure if an task / ToDo manager can be "advanced" without a desktop companion, or tight integration with one. Mobiles are handy, but not where work actually

Not sure if an task / ToDo manager can be "advanced" without a desktop companion, or tight integration with one. Mobiles are handy, but not where work actually gets done. So far, I have not warmed up to web based task managers, which lack the convenience that a local app can provide: hot key integration, interop with local calendars, mail, etc.