All good contributions, but before spending an infinite amount of time (and one can ...) trying to mine ADV:
- When were you planning to do this - approximately? If you are seeking advice, I would suggest after "labour Day", but not too far in to September, as it can snow (substantially) in these areas by then. In summer (being more or less defined in the US as the period between Memorial Day and labour Day), the national parks and areas - as you may imagine - are inundated with tourists. The later in the season (closer to labour Day), the worse it is. Early June is probably less than ideal as well, as it can still be fairly cool (snow on ground/can snow) in these areas.
- Going it alone, or do you have a group?
- How would you prefer to overnight? Lodges, hotels/motels, or tent/camping? It matters, in that some bikes are more well suited to stowing. carrying, and unpacking gear needed for camping. There's the matter of said camping gear, and bringing all that across may not be practical ...
- Have you considered signing up for a guided tour - all inclusive kind of thing? I know that this suggestion may not seem part of the SDer ethos, but some of these programs are not only impressively well organized, but allow ample freedom, and are generally very civilized in accommodation arrangement, no matter how "rustic". This allows one to focus more on the ride and their holiday, than the logistics.
- What kind of bike do you prefer? If you have zero plans to head off road at all, there's no need for a DS/Adventure bike. Who knows - maybe you prefer touring on a cruiser - ? I ask, in that we can then point you to some resources for rentals. Of note, starting in Colorado may be your best bet for this - probably the most offerings and greatest variety of bike rentals, tour services, etc. outside California. In Canada, everything is likely to cost more.
Give us some specifics on what your ideal arrangements might be, and I'm sure many here will be able contribute.