Any tips would be appreciated.
With three weeks I will be a bit limited. Three weeks is a lot of time. Plenty of time. You're not trying to see the whole country after all.
What are the speed limits? Most limits are about 65 miles per hour posted (105 KPH). In urban areas and major freeways speeds are up to 80 MPH (129 KPH) (not posted, but what people actually drive). Gauge the average rate of traffic around you and go that speed, or a little faster or slower. OK, faster.
What accommodation is suggested? Motel 8 is very reasonable and clean. They are located throughout the US. Avoid Motel 6 (cheapest; used by prostitutes, porn directors, and drug dealers, or so I've heard). BTW, California is the only state in which you can legally share lanes with cars (go up between them in slow or stopped traffic).
The important thing is to travel out of your peak vacation seasons. Unlike Europe, where everyone vacations in the same month, US vacations cluster around major holidays. The biggest travel holidays are Thanksgiving (late November) and Christmas. Also, July 4 weekend (Independence Day), Memorial Day weekend (late May), and Labor Day weekend (early September). Apart from that, there will be moderate travel all through summer, but no big crush of people (except at the usual spots, like Disneyland).
I hate the rain, so perhaps where it is a dryish climate. Rain sucks. As a native Californian, I don't really understand rain. Here it rains in the winter months, and then doesn't rain at all in the summer and most of the sprig and fall. It seems to me that in all other states (maybe not Florida), it can rain, and hard, any time during the year. That includes (especially) Oregon and Washington. So if it's no rain you want, then California's your place. Don't forget our seasons are reversed from yours. Our summer is June, July, August. Our winter is December, January, February.
Where would be a good touring area and what time of the year weather wise is recommended? I would like to be out of any big cities where possible and in an area offering good biking country. and and not flat nor too many monotonous roads. I know California best, so that is what I can talk about. But the fact is, it meets your criteria.
Just here in the Bay Area or within a few hours we have access to some of the best motorcycling venues in the world (yes, the world), as wells as major international tourist destinations. We have:
San Francisco and the Golden Gate Bridge:
The Sierra Nevada Mountains, and Yosemite:
Highway 1 Along the Coast:
The Gold Country with its Old West Towns in the Sierra Nevada Foothills:
To the South, Los Angeles and All Its Sites:
What are the more famous routes around the country and a bit of a write up on them.
Again, Highway 1, a must-see if you're a motorcyclist.
In summary, California offers good weather, international destinations, diverse scenery (ocean, mountains, desert, Wine country, Gold Country, Yosemite), and well-maintained, twisty motorcycle roads.
Best,
JB