Garmin's Forerunner 301 looks interesting for bike and running use. I've never used one, but a friend has the Forerunner 201 (no HRM) and is happy with it.
For HRM use on a bike, it's hard to beat the Polar S720/S725 HRMs. They pretty much do it all and are the standard. For running, they won't measure distance, but that's what TopoUSA software or a low cost eTrex GPS is for.