You pm'd me with some questions about a trip from Lassen to Crater Lake. I'm replying here because your profile has messages blocked.
Sacramento is a good place to start, being relatively close to Lassen. If you aren’t including San Francisco in this trip, you avoid the congestion of the Bay Area. Sacramento Metro Airport isn’t even in the main part of town, so you miss that urban congestion too.
First things first: this trip is best done in summer. Of these places, Lassen is the one I know best, and it has one of the shortest visitor seasons of any California national park because of the high elevations (and Mt. Shasta is higher). After the first big snow, Hwy 89, the main park road (and the only one that goes through the entire park) is closed. Among state highways, it’s basically a scenic detour that doesn’t really “go anywhere,” so it isn’t essential to keep it open. It can be snowed in until June, maybe even July, and I’ve seen snow along the roadside on Hwy 89 as late as August. So before buying any tickets, check with the park to make sure the roads are open, including side roads to sights you might want to see.
From Sacto to Crater Lake, you have some choice of routes, and you might think about going one way and returning another. To keep this uncomplicated, I’ll presume you’re going from Sacto to Lassen, Shasta, then Crater Lake, but an alternative is to see either Lassen or Shasta on the way up and the other coming back, to break up the 360-370 miles between Sacto and Crater Lake. The basic route is I-5. The biggest towns with services en route to Lassen are Williams, Willows, and Red Bluff. Red Bluff is where you turn off; the south end of town as you enter isn’t very appealing, but farther north is the charming historic downtown with businesses and homes in preserved buildings. You cross the Sacramento River on the Hwy 36 bridge.
You could see much of Lassen in a day, although more time is good if you have it. There are several campgrounds but only one lodge in the park, and it (Drakesbad Resort) is not on the main road out of Red Bluff. It’s accessed only by a side road from the town of Chester. It’s very popular, so you might or might not find any openings. The nearest motels or cabins outside the park are around the hamlet of Mineral.
On your way in from the south, you’ll come to the new visitor center (just opened; I haven’t seen it yet). A little farther is Sulphur Works, an area of volcanic activity where you can smell the sulphur and see and hear the steam, bubbling mud, and other geothermal signals. It’s just a hint of what you’ll see at Bumpass Hell, which scientists consider the most active volcanic area in the U.S. outside of Alaska, Hawaii, and Yellowstone. Bumpass Hell is about 1.5 mile each way from the parking area, with some elevation gain and loss, but most healthy people will be fine (I’ve seen kids of 8-9 on it). There are also hikes in the park to lakes and other volcanic features, and of course the Lassen Peak climb.
Most people leave Lassen toward Redding, but a scenic alternative would be to stay on 89 through McCloud, one of the gateway towns for Mt. Shasta. This stretch is very rural through a lot of national forest lands, with almost no towns or services.
Sidebar: Coming out of Sacto, you could bypass I-5 and take CA 70 and then CA 99. These are more leisurely than the interstate, and you’ll go through several medium sized towns including Chico. This road meets Hwy 36 east of Red Bluff and you don’t cross the Sacramento River.
Either way, you end up on I-5 and you’ll see Mt. Shasta for miles. It’s the dominating feature of the landscape (just as Lassen is farther south). It has snow on top all the time; it’s less than 350 ft. lower in elevation than Mt. Whitney, California’s highest peak. There are several towns around it that cater to Shasta visitors, especially promoting its mystical side. It’s important in Native American lore, and many modern “new age” enthusiasts attribute special qualities to it. These towns include McCloud, Dunsmuir, Mount Shasta, and Weed, which have most visitor services.
I am not that knowledgeable about Mt. Shasta. If you ask on the Mt. Shasta forum, or Dunsmuir or Weed, you’ll get more detailed info than I can give you. One thing about Shasta: access to it is harder than for Lassen. Many of the ways to it are service roads, fire roads, etc. The agency with jurisdiction is the U.S. Forest Service, not the National Park Service like Lassen, and the Forest Service is not as much about visitation as the Park Service.
The direct way from I-5 in CA to Crater Lake is to turn off at the town of Weed. You’ll be on a CA then an OR state highway that goes to Klamath Falls, the gateway town for Crater Lake.
Like Lassen, you could see the main sights in Crater Lake National Park in a day, but you might want to stay longer. There are places to stay within the park, and even if you don’t do so, try to have lunch at Crater Lake Lodge. It’s a classic historic park resort with a grand view of the lake from the dining rooms or the verandah. This is a very intriguing park: the deepest lake in the U.S., all tucked away snug inside the crater of an extinct volcano. There is some snow someplace in the park most of the year. There are tiny islands in the lake, a formation that looks like a ghost ship, and more. A road goes all the way around it and goes to all the places of interest. One of the most fascinating to me was the Pinnacles, a cluster of tall, sharp volcanic rock formations.
From Crater Lake to Sacto, you can come back the same way, or go over to Medford. Honestly, it isn’t that exciting a city. But there is a historic mining town near it called Jacksonville, which has a wonderful historic district. It easily rivals some of the best California Gold Rush towns in historic preservation, and it isn’t as touristy as some of the California places. From Medford, I-5 goes all the way back.
As for your question about time, I think 7 days would be enough. You’d get to Lassen or that area the same day you fly in, maybe spend a night or even two there, spend a night around Shasta, a night or two at Crater Lake, perhaps a night somewhere on your way back, and that still gives you some leeway and you wouldn’t be rushed.