All Garmin Edge models can be used without any sort of online account. As can any of the outdoor models, eg the Etrex, Oregon etc. There is a handlebar mount available for these, so you can use them on your bike if you want.
Newer Garmin models work as a USB mass storage device. ie you plug it into your computer, and it appears as a disk drive. So you can just copy files on and off, usually in FIT, TCX or GPX format.
Some models also have the option of Bluetooth or wifi for uploading. These will require a Garmin Connect account, and the app on a phone or tablet. But you don't have to use this, you can just plug in a USB cable as above.
There is a variety of free software you can use on your own computer for viewing rides etc, eg
- TurtleSport - fairly simple, lets you view rides on a map, and basic statistics
- GoldenCheetah - good for more detailed analysis of power etc
- Garmin Training Center - now discontinued, may not work properly with newer devices
For plotting routes, to transfer to the GPS. Depends on what sort of maps you want to use, some options include
- Garmin BaseCamp
Also some websites will let you draw a route, then save it as a file, without an account. eg GPSies
For updating the firmware, you can use Garmin WebUpdater software.