I would have responded sooner had this been posed to the Camcorders forum.
It will be useful to know what OS is running on your iMac, but since you are using iMovie 10 you should be OK.
We assume you can see the AVCHD video file on the HG21.
1a) Connect the HG21's USB port to the Mac's USB port. Power up the HG21. This should put the HG21 into USB mode. If not, use the HG21's option menu to put it into USB mode. This should mount the storage in the HG21 to the Mac's desktop.
1b) Alternatively, take the SD card out of the HG21 and put it in the iMac's SD card reader. The flash memory card will mount to the Mac's desktop.
If your Mac does not have a built-in SD card reader, use an external SD card reader. I have a 20-in-1 reader that connects using a USB cable - I think it was $6 at Fry's.
Whether 1 or 1b, locate the AVCHD file and copy it to the Mac's hard drive. After copying, drag the SD card to the trash to dismount that volume and remove the card from the card reader.
2) Define "viewable file". Assuming the iMac's operating system is relatively current, that means QuickTime will also be current. Work with the file that was copied to the Mac's hard drive. When you double-click on the AVCHD-compressed video file, QuickTime should launch. A window that looks a bit like an open folder will open. There will be thumbnails of all the video clips in that AVCHD file. If you double click a video clip, that clip will open in a window and can be played back - it is a "viewable file" on the iMac.
Quit - then reopen that AVCHD file. All the video clips in the window again. This time, single click on a video clip to select it. At the command line under "File", I think, you can export that single clip to a stand-alone, QuickTime (MOV) file.
Double click that MOV file for playback. This is a "viewable file", no longer AVCHD compressed. In theory, can be played back on a Windows computer with a current version of QuickTime or other current media player that can deal with uncompressed HD video in a MOV file.
The AVCHD comprised file copied from the camcorder to the Mac is the original file and handy for back-up. The uncompressed standalone MOV file is suitable for use in any video editor capable of dealing with h.264 format MOV video files (whether Mac or Windows.
3) Using iMovie 10.x or Final Cut Pro:
Using the AVCHD file: Launch iMovie. Import the video. Under File, Import, navigate to the AVCHD file and select it.
Using the standalone MOV file: Launch iMovie. Drag the MOV file to the Library. You can use Import if you want.
4) If you want to convert the video using something other than QuickTime, HandBrake and MPEG StreamClip are both open source and cross-platform (macOS & Windows).
5) Please define "better" relative to a video editing app. iMovie comes with all Macs. It is considered a "basic" editor, but is robust in its feature set. Final Cut Pro has a similar look/feel but is "pro grade". Color-grading and a bunch of other features aside, the most useful features I use are multiple video and audio tracks stacked in the timeline, "scaling" and positioning.
In iMovie (as with Windows MovieMaker), the timeline can deal with one video file at the same time. Yes, there can be multiple video files (or JPEG or PDF, etc) throughout the entire duration of a video project, but you can't "stack" the files. For example, lets say you have three cameras running at the same time of a car being driven. Camera 1 is on the car facing forward. Camera 2 is in the car pointed at the driver and camera 3 is at the end of a street following the car as it approaches. Using iMovie, it is challenging (but very possible) to synch the different cameras, then cut to the different camera views. (It is entirely possible that iMovie has added multiple simultaneous cameras as a feature - I have not used it extensively, recently, so I could be incorrect on this paragraph.)
With Final Cut Pro, you can "stack" the video... using the 3-camera example from the last paragraph, using FCP, all three videos can be in the same video window at the same time... After importing the videos to the Library, drag them to the timeline. In the timeline, synch them, scale them to ~40% then position them in the video window so all three are visible simultaneously. Adjust positions, audio, scaling, etc...
If you certain specific functionality, tell us what that is so we know why an editor is "better" for what you need.
Macintosh computers have been dealing with AVCHD files for *many* years. My first experience with AVCHD files from a Canon camcorder (an HF R-something) imported for editing on a Mac dates back to around 2008... and have been using Macs for a few years before that.
My set up:
iMac 21.5 inch from Late 2012.
8 gig RAM.
External drives (USB and firewire) for video project storage.
Used to use iMovie; Currently use Final Cut Pro.
macOS Sierra (10.12.6)
QuickTime Player (10.4)
MPEG StreamClip (1.9.3b
HandBrake 0.10.2 x86_64
I have used various Canon camcorders in the past (XC10, HF-R and HG-series). My current gear is Sony-centric (HDR-AX2000; PXW-Z150, Sony HDR-AS30v).